## Hypothesis Testing with Minitab: A Comprehensive Guide

Welcome to this comprehensive guide on hypothesis testing with Minitab. In this article, we will delve deep into the world of hypothesis testing and explore how Minitab, a powerful statistical software, can assist us in conducting hypothesis tests effectively. Whether you are a beginner or an experienced user of Minitab, this guide will provide you with a detailed understanding of hypothesis testing and its implementation using Minitab.

## 1. Introduction to Hypothesis Testing

In this section, we will introduce the concept of hypothesis testing and its significance in statistical analysis. We will discuss the basic terminology such as null hypothesis, alternative hypothesis, significance level, p-value, and type I and type II errors. Understanding these concepts is crucial for grasping the essence of hypothesis testing.

## 1.1 Null Hypothesis and Alternative Hypothesis

Here, we will define the null hypothesis and alternative hypothesis and explain their roles in hypothesis testing. We will also discuss how to formulate these hypotheses based on the research question or problem at hand.

## 1.2 Significance Level and P-value

In this subtopic, we will explore the significance level and p-value, which are essential components of hypothesis testing. We will explain how the significance level determines the threshold for accepting or rejecting the null hypothesis, and how the p-value helps us assess the strength of evidence against the null hypothesis.

## 1.3 Type I and Type II Errors

We will discuss the concept of type I and type II errors, which are errors that can occur during hypothesis testing. We will explain the consequences of committing these errors and how they are related to the significance level and power of a statistical test.

## 2. Hypothesis Testing Process

In this section, we will outline the step-by-step process of hypothesis testing. We will cover the following subtopics:

## 2.1 Formulating the Research Question

We will discuss how to formulate a clear research question that can be tested using hypothesis testing. We will provide examples to illustrate the process of formulating a research question.

## 2.2 Choosing the Appropriate Hypothesis Test

Here, we will explore the different types of hypothesis tests available in Minitab and discuss the criteria for selecting the most appropriate test for a given research question. We will provide guidelines and examples to facilitate the selection process.

## 2.3 Collecting and Preparing Data

In this subtopic, we will discuss the importance of collecting and preparing data for hypothesis testing. We will explore the various data collection methods and techniques, as well as the steps involved in preparing the data for analysis in Minitab.

## 2.4 Conducting the Hypothesis Test

Here, we will dive into the actual process of conducting a hypothesis test using Minitab. We will explain how to input the data, specify the null and alternative hypotheses, select the appropriate test options, and interpret the results obtained from Minitab.

## 2.5 Interpreting the Results

In this subtopic, we will discuss how to interpret the output generated by Minitab after conducting a hypothesis test. We will guide you through the process of analyzing the p-value, making a decision based on the significance level, and drawing conclusions from the results.

## 3. Advanced Topics in Hypothesis Testing with Minitab

In this section, we will explore some advanced topics and techniques related to hypothesis testing using Minitab. We will cover the following subtopics:

## 3.1 One-Sample Hypothesis Tests

Here, we will focus on one-sample hypothesis tests, which involve comparing the mean or proportion of a single sample to a known or hypothesized value. We will discuss the various tests available in Minitab for one-sample scenarios and provide detailed examples.

## 3.2 Two-Sample Hypothesis Tests

In this subtopic, we will shift our attention to two-sample hypothesis tests, which involve comparing the means or proportions of two independent samples. We will explore the different types of two-sample tests in Minitab and provide practical examples to illustrate their applications.

## 3.3 Paired-Sample Hypothesis Tests

Here, we will explore paired-sample hypothesis tests, which involve comparing the means of two related samples. We will explain the concept of paired samples and discuss how to perform paired-sample tests in Minitab. Real-world examples will be provided to enhance understanding.

## 3.4 Power and Sample Size Calculations

In this subtopic, we will discuss the concepts of power and sample size calculations in hypothesis testing. We will explain how to determine the sample size required to achieve a desired level of power, as well as how to calculate the power of a statistical test using Minitab.

## 4. Frequently Asked Questions (FAQs)

4.1 faq 1: can i use minitab for hypothesis testing if i have a small sample size.

Yes, Minitab can be used for hypothesis testing even with small sample sizes. However, it is important to consider the limitations and potential impact on the power of the test. Minitab provides options for calculating power and sample size, which can help you determine the appropriate sample size for your study.

## 4.2 FAQ 2: How can I interpret the p-value obtained from a hypothesis test in Minitab?

The p-value represents the probability of obtaining the observed data, or more extreme data, assuming that the null hypothesis is true. If the p-value is less than the significance level (usually 0.05), it provides evidence against the null hypothesis, suggesting that there is a statistically significant difference or relationship. Conversely, if the p-value is greater than the significance level, there is insufficient evidence to reject the null hypothesis.

## 4.3 FAQ 3: Can Minitab handle hypothesis tests for nonparametric data?

Yes, Minitab offers a range of nonparametric tests for hypothesis testing when the data do not meet the assumptions of parametric tests. These tests include the Wilcoxon rank-sum test, Kruskal-Wallis test, and Mann-Whitney test, among others. Minitab provides easy-to-use options for conducting nonparametric tests and interpreting the results.

## 5. Conclusion

In conclusion, hypothesis testing is a fundamental tool in statistical analysis, and Minitab provides a robust platform for conducting hypothesis tests with ease and accuracy. This comprehensive guide has covered the essential concepts, steps, and techniques involved in hypothesis testing using Minitab. By following the guidelines and examples provided, you can confidently apply hypothesis testing in your research projects or data analysis tasks. Remember to carefully interpret the results and consider the limitations and assumptions of the tests. With Minitab, you have a powerful ally in your statistical journey.

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## 8.1.2.2 - Minitab: Hypothesis Tests for One Proportion

A hypothesis test for one proportion can be conducted in Minitab. This can be done using raw data or summarized data.

- If you have a data file with every individual's observation, then you have raw data .
- If you do not have each individual observation, but rather have the sample size and number of successes in the sample, then you have summarized data.

The next two pages will show you how to use Minitab to conduct this analysis using either raw data or summarized data .

Note that the default method for constructing the sampling distribution in Minitab is to use the exact method. If \(np_0 \geq 10\) and \(n(1-p_0) \geq 10\) then you will need to change this to the normal approximation method. This must be done manually. Minitab will use the method that you select, it will not check assumptions for you!

## 8.1.2.2.1 - Minitab: 1 Proportion z Test, Raw Data

If you have data in a Minitab worksheet, then you have what we call "raw data." This is in contrast to "summarized data" which you'll see on the next page.

In order to use the normal approximation method both \(np_0 \geq 10\) and \(n(1-p_0) \geq 10\). Before we can conduct our hypothesis test we must check this assumption to determine if the normal approximation method or exact method should be used. This must be checked manually. Minitab will not check assumptions for you.

In the example below, we want to know if there is convincing evidence that the proportion of students who are male is different from 0.50.

\(n=226\) and \(p_0=0.50\)

\(np_0 = 226(0.50)=113\) and \(n(1-p_0) = 226(1-0.50)=113\)

Both \(np_0 \geq 10\) and \(n(1-p_0) \geq 10\) so we can use the normal approximation method.

## Minitab ® – Conducting a One Sample Proportion z Test: Raw Data

Research question: Is the proportion of students who are male different from 0.50?

- class_survey.mpx
- In Minitab, select Stat > Basic Statistics > 1 Proportion
- Select One or more samples, each in a column from the dropdown
- Double-click the variable Biological Sex to insert it into the box
- Check the box next to Perform hypothesis test and enter 0.50 in the Hypothesized proportion box
- Select Options
- Use the default Alternative hypothesis setting of Proportion ≠ hypothesized proportion value
- Use the default Confidence level of 95
- Select Normal approximation method
- Click OK and OK

The result should be the following output:

Event: Biological Sex = Male p: proportion where Biological Sex = Male Normal approximation is used for this analysis.

N | Event | Sample p | 95% CI for p |
---|---|---|---|

226 | 99 | 0.438053 | (0.373368, 0.502738) |

Null hypothesis | H : p = 0.5 |
---|---|

Alternative hypothesis | H : p ≠ 0.5 |

Z-Value | P-Value |
---|---|

-1.86 | 0.063 |

## Summary of Results

We could summarize these results using the five-step hypothesis testing procedure:

\(np_0 = 226(0.50)=113\) and \(n(1-p_0) = 226(1-0.50)=113\) therefore the normal approximation method will be used.

\(H_0\colon p = 0.50\)

\(H_a\colon p \ne 0.50\)

From the Minitab output, \(z\) = -1.86

From the Minitab output, \(p\) = 0.0625

\(p > \alpha\), fail to reject the null hypothesis

There is NOT enough evidence that the proportion of all students in the population who are male is different from 0.50.

## 8.1.2.2.2 - Minitab: 1 Sample Proportion z test, Summary Data

Example: overweight.

The following example uses a scenario in which we want to know if the proportion of college women who think they are overweight is less than 40%. We collect data from a random sample of 129 college women and 37 said that they think they are overweight.

First, we should check assumptions to determine if the normal approximation method or exact method should be used:

\(np_0=129(0.40)=51.6\) and \(n(1-p_0)=129(1-0.40)=77.4\) both values are at least 10 so we can use the normal approximation method.

## Minitab ® – Performing a One Proportion z Test with Summarized Data

To perform a one sample proportion z test with summarized data in Minitab:

- Select Summarized data from the dropdown
- For number of events, add 37 and for number of trials add 129.
- Check the box next to Perform hypothesis test and enter 0.40 in the Hypothesized proportion box
- Use the default Alternative hypothesis setting of Proportion < hypothesized proportion value

Event: Event proportion Normal approximation is used for this analysis.

N | Event | Sample p | 95% Upper Bound for p |
---|---|---|---|

129 | 37 | 0.286822 | 0.352321 |

Null hypothesis | H : p = 0.4 |
---|---|

Alternative hypothesis | H : p < 0.4 |

Z-Value | P-Value |
---|---|

-2.62 | 0.004 |

\(H_0\colon p = 0.40\)

\(H_a\colon p < 0.40\)

From output, \(z\) = -2.62

From output, \(p\) = 0.004

\(p \leq \alpha\), reject the null hypothesis

There is convincing evidence that the proportion of women in the population who think they are overweight is less than 40%.

## 8.1.2.2.2.1 - Minitab Example: Normal Approx. Method

Example: gym membership.

Research question: Are less than 50% of all individuals with a membership at one gym female?

A simple random sample of 60 individuals with a membership at one gym was collected. Each individual's biological sex was recorded. There were 24 females.

First we have to check the assumptions:

np = 60 (0.50) = 30

n(1-p) = 60(1-0.50) = 30

The assumptions are met to use the normal approximation method.

- For number of events, add 24 and for number of trials add 60.

N | Event | Sample p | 95% Upper Bound for p |
---|---|---|---|

60 | 24 | 0.400000 | 0.504030 |

Null hypothesis | H : p = 0.5 |
---|---|

Alternative hypothesis | H : p < 0.5 |

Z-Value | P-Value |
---|---|

-1.55 | 0.061 |

\(np_0=60(0.50)=30\) and \(n(1-p_0)=60(1-0.50)=30\) both values are at least 10 so we can use the normal approximation method.

\(H_0\colon p = 0.50\)

\(H_a\colon p < 0.50\)

From output, \(z\) = -1.55

From output, \(p\) = 0.061

\(p \geq \alpha\), fail to reject the null hypothesis

There is not enough evidence to support the alternative that the proportion of women memberships at this gym is less than 50%.

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## How to Perform a Normality Test on Minitab

Last Updated: January 31, 2020

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, volunteer authors worked to edit and improve it over time. This article has been viewed 37,848 times.

Before you start performing any statistical analysis on the given data, it is important to identify if the data follows normal distribution. If the given data follows normal distribution, you can make use of parametric tests (test of means) for further levels of statistical analysis. If the given data does not follow normal distribution, you would then need to make use of non-parametric tests (test of medians). As we all know, parametric tests are more powerful than non-parametric tests. Hence, checking the normality of the given data becomes all the more important.

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## Understanding Analysis of Variance (ANOVA) and the F-test

Topics: ANOVA , Hypothesis Testing , Data Analysis

Analysis of variance (ANOVA) can determine whether the means of three or more groups are different. ANOVA uses F-tests to statistically test the equality of means. In this post, I’ll show you how ANOVA and F-tests work using a one-way ANOVA example.

But wait a minute...have you ever stopped to wonder why you’d use an analysis of variance to determine whether means are different? I'll also show how variances provide information about means.

As in my posts about understanding t-tests , I’ll focus on concepts and graphs rather than equations to explain ANOVA F-tests.

## What are F-statistics and the F-test?

F-tests are named after its test statistic, F, which was named in honor of Sir Ronald Fisher. The F-statistic is simply a ratio of two variances. Variances are a measure of dispersion, or how far the data are scattered from the mean. Larger values represent greater dispersion.

Variance is the square of the standard deviation. For us humans, standard deviations are easier to understand than variances because they’re in the same units as the data rather than squared units. However, many analyses actually use variances in the calculations.

F-statistics are based on the ratio of mean squares. The term “ mean squares ” may sound confusing but it is simply an estimate of population variance that accounts for the degrees of freedom (DF) used to calculate that estimate.

Despite being a ratio of variances, you can use F-tests in a wide variety of situations. Unsurprisingly, the F-test can assess the equality of variances. However, by changing the variances that are included in the ratio, the F-test becomes a very flexible test. For example, you can use F-statistics and F-tests to test the overall significance for a regression model , to compare the fits of different models, to test specific regression terms, and to test the equality of means.

## Using the F-test in One-Way ANOVA

To use the F-test to determine whether group means are equal, it’s just a matter of including the correct variances in the ratio. In one-way ANOVA, the F-statistic is this ratio:

F = variation between sample means / variation within the samples

The best way to understand this ratio is to walk through a one-way ANOVA example.

We’ll analyze four samples of plastic to determine whether they have different mean strengths. (If you don't have Minitab, you can download a free 30-day trial .) I'll refer back to the one-way ANOVA output as I explain the concepts.

In Minitab, choose Stat > ANOVA > One-Way ANOVA... In the dialog box, choose "Strength" as the response, and "Sample" as the factor. Press OK, and Minitab's Session Window displays the following output:

## Numerator: Variation Between Sample Means

One-way ANOVA has calculated a mean for each of the four samples of plastic. The group means are: 11.203, 8.938, 10.683, and 8.838. These group means are distributed around the overall mean for all 40 observations, which is 9.915. If the group means are clustered close to the overall mean, their variance is low. However, if the group means are spread out further from the overall mean, their variance is higher.

Clearly, if we want to show that the group means are different, it helps if the means are further apart from each other. In other words, we want higher variability among the means.

Imagine that we perform two different one-way ANOVAs where each analysis has four groups. The graph below shows the spread of the means. Each dot represents the mean of an entire group. The further the dots are spread out, the higher the value of the variability in the numerator of the F-statistic.

What value do we use to measure the variance between sample means for the plastic strength example? In the one-way ANOVA output, we’ll use the adjusted mean square (Adj MS) for Factor, which is 14.540. Don’t try to interpret this number because it won’t make sense. It’s the sum of the squared deviations divided by the factor DF. Just keep in mind that the further apart the group means are, the larger this number becomes.

## Denominator: Variation Within the Samples

We also need an estimate of the variability within each sample. To calculate this variance, we need to calculate how far each observation is from its group mean for all 40 observations. Technically, it is the sum of the squared deviations of each observation from its group mean divided by the error DF.

If the observations for each group are close to the group mean, the variance within the samples is low. However, if the observations for each group are further from the group mean, the variance within the samples is higher.

In the graph, the panel on the left shows low variation in the samples while the panel on the right shows high variation. The more spread out the observations are from their group mean, the higher the value in the denominator of the F-statistic.

If we’re hoping to show that the means are different, it's good when the within-group variance is low. You can think of the within-group variance as the background noise that can obscure a difference between means.

For this one-way ANOVA example, the value that we’ll use for the variance within samples is the Adj MS for Error, which is 4.402. It is considered “error” because it is the variability that is not explained by the factor.

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## The F-Statistic: Variation Between Sample Means / Variation Within the Samples

The F-statistic is the test statistic for F-tests. In general, an F-statistic is a ratio of two quantities that are expected to be roughly equal under the null hypothesis, which produces an F-statistic of approximately 1.

The F-statistic incorporates both measures of variability discussed above. Let's take a look at how these measures can work together to produce low and high F-values. Look at the graphs below and compare the width of the spread of the group means to the width of the spread within each group.

The low F-value graph shows a case where the group means are close together (low variability) relative to the variability within each group. The high F-value graph shows a case where the variability of group means is large relative to the within group variability. In order to reject the null hypothesis that the group means are equal, we need a high F-value.

For our plastic strength example, we'll use the Factor Adj MS for the numerator (14.540) and the Error Adj MS for the denominator (4.402), which gives us an F-value of 3.30.

Is our F-value high enough? A single F-value is hard to interpret on its own. We need to place our F-value into a larger context before we can interpret it. To do that, we’ll use the F-distribution to calculate probabilities.

## F-distributions and Hypothesis Testing

For one-way ANOVA, the ratio of the between-group variability to the within-group variability follows an F-distribution when the null hypothesis is true.

When you perform a one-way ANOVA for a single study, you obtain a single F-value. However, if we drew multiple random samples of the same size from the same population and performed the same one-way ANOVA, we would obtain many F-values and we could plot a distribution of all of them. This type of distribution is known as a sampling distribution .

Because the F-distribution assumes that the null hypothesis is true, we can place the F-value from our study in the F-distribution to determine how consistent our results are with the null hypothesis and to calculate probabilities.

The probability that we want to calculate is the probability of observing an F-statistic that is at least as high as the value that our study obtained. That probability allows us to determine how common or rare our F-value is under the assumption that the null hypothesis is true. If the probability is low enough, we can conclude that our data is inconsistent with the null hypothesis. The evidence in the sample data is strong enough to reject the null hypothesis for the entire population.

This probability that we’re calculating is also known as the p-value!

To plot the F-distribution for our plastic strength example, I’ll use Minitab’s probability distribution plots . In order to graph the F-distribution that is appropriate for our specific design and sample size, we'll need to specify the correct number of DF. Looking at our one-way ANOVA output, we can see that we have 3 DF for the numerator and 36 DF for the denominator.

The graph displays the distribution of F-values that we'd obtain if the null hypothesis is true and we repeat our study many times. The shaded area represents the probability of observing an F-value that is at least as large as the F-value our study obtained. F-values fall within this shaded region about 3.1% of the time when the null hypothesis is true. This probability is low enough to reject the null hypothesis using the common significance level of 0.05. We can conclude that not all the group means are equal.

Learn how to correctly interpret the p-value.

## Assessing Means by Analyzing Variation

ANOVA uses the F-test to determine whether the variability between group means is larger than the variability of the observations within the groups. If that ratio is sufficiently large, you can conclude that not all the means are equal.

This brings us back to why we analyze variation to make judgments about means. Think about the question: "Are the group means different?" You are implicitly asking about the variability of the means. After all, if the group means don't vary, or don't vary by more than random chance allows, then you can't say the means are different. And that's why you use analysis of variance to test the means.

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## Method table for One-Way ANOVA

In this topic, null hypothesis and alternative hypothesis, significance level, equal variances.

One-way ANOVA is a hypothesis test that evaluates two mutually exclusive statements about two or more population means. These two statements are called the null hypothesis and the alternative hypotheses. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

- The null hypothesis (H 0 ) is that the group means are all equal.
- The alternative hypothesis (H A ) is that not all group means are equal.

## Interpretation

Compare the p-value to the significance level to determine whether to reject the null hypothesis.

The significance level (denoted by alpha or α) is the maximum acceptable level of risk for rejecting the null hypothesis when the null hypothesis is true (type I error).

Use the significance level to decide whether to reject or fail to reject the null hypothesis (H 0 ). When the p-value is less than the significance level, the usual interpretation is that the results are statistically significant, and you reject H 0 .

For one-way ANOVA, you reject the null hypothesis when there is sufficient evidence to conclude that not all of the means are equal.

The Method table indicates whether Minitab assumes that the population variances for all groups are equal.

Look in the standard deviation (StDev) column of the one-way ANOVA output to determine whether the standard deviations are approximately equal.

If you cannot assume equal variances, deselect Assume equal variances in the Options sub-dialog box for One-Way ANOVA . In this case, Minitab performs Welch's test, which performs well when the variances are not equal.

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## IMAGES

## COMMENTS

Null hypothesis (H 0) The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge. The alternative hypothesis states that a population parameter is smaller ...

Specify the hypotheses. First, the manager formulates the hypotheses. The null hypothesis is: The population mean of all the pipes is equal to 5 cm. Formally, this is written as: H 0: μ = 5. Then, the manager chooses from the following alternative hypotheses: Condition to test. Alternative Hypothesis. The population mean is less than the target.

Introduction to Hypothesis Tests ( Single Sample Tests)

A hypothesis test is rule that specifies whether to accept or reject a claim about a population depending on the evidence provided by a sample of data. A hypothesis test examines two opposing hypotheses about a population: the null hypothesis and the alternative hypothesis. The null hypothesis is the statement being tested.

How to conduct one sample Hypothesis Tests in Minitab

Once we have this, we can then work on defining our Null and Alternative Hypotheses. The null hypothesis is always the option that maintains the status quo and results in the least amount of disruption, hence it is "Busy Doin' Nothin'". When the probability of the Null Hypothesis is very low and we reject the Null Hypothesis, then we will ...

Select Stat > Basic Stat > 1 Sample t. Choose the summarized data option and enter 40 for "Sample size", 11 for the "Sample mean", and 3 for the "Standard deviation". Check the box for "Perform Hypothesis Test" and enter the null value of 10. Click Options . With our stated alpha value of 5% we keep the default confidence level of 95.

If you're already up on your statistics, you know right away that you want to use a 2-sample t-test, which analyzes the difference between the means of your samples to determine whether that difference is statistically significant. You'll also know that the hypotheses of this two-tailed test would be: Null hypothesis: H0: m1 - m2 = 0 (strengths ...

Conversely, if the p-value is greater than the significance level, there is insufficient evidence to reject the null hypothesis. 4.3 FAQ 3: Can Minitab handle hypothesis tests for nonparametric data? Yes, Minitab offers a range of nonparametric tests for hypothesis testing when the data do not meet the assumptions of parametric tests.

Hypothesis testing is a standard procedure to test a claim or a statement. It is extremely important to realize that we are not making definitive conclusions. We are giving probabilistic ...

T-tests are handy hypothesis tests in statistics when you want to compare means. You can compare a sample mean to a hypothesized or target value using a one-sample t-test. You can compare the means of two groups with a two-sample t-test. If you have two groups with paired observations (e.g., before and after measurements), use the paired t-test.

1-Sample Sign. Perform a hypothesis test, enter a test median, and select the alternative hypothesis. To perform a hypothesis test, select Test median and enter a value. Use a hypothesis test to determine whether the population median (denoted as η) differs significantly from the hypothesized median (denoted as η0) that you specify.

Research question: Is there a relationship between where a student sits in class and whether they have ever cheated?. Null hypothesis: Seat location and cheating are not related in the population.; Alternative hypothesis: Seat location and cheating are related in the population.; To perform a chi-square test of independence in Minitab using raw data: Open Minitab file: class_survey.mpx

Example 1: Weight of Turtles. A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles. Here is how to write the null and alternative hypotheses for this scenario: H0: μ = 300 (the true mean weight is equal to ...

In Minitab, select Stat > Basic Statistics > 1 Proportion. Select One or more samples, each in a column from the dropdown. Double-click the variable Biological Sex to insert it into the box. Check the box next to Perform hypothesis test and enter 0.50 in the Hypothesized proportion box. Select Options.

For example, if the p-value was 0.02 (as in the Minitab output below) and we're using an alpha of 0.05, we'd reject the null hypothesis and conclude that the average price of Cairn terrier is NOT $400. If the p-value is low, the null must go. Alternatively, if the p-value is greater than alpha, then we fail to reject the null hypothesis.

If the absolute value of the t-value is greater than the critical value, you reject the null hypothesis. If the absolute value of the t-value is less than the critical value, you fail to reject the null hypothesis. You can calculate the critical value in Minitab or find the critical value from a t-distribution table in most statistics books.

The null and three alternative hypotheses for a one-sample t-test are shown below: The default alternative hypothesis is the last one listed: The true population mean is not equal to the mean of the sample, and this is the option used in this example. To understand the calculations, we'll use a sample data set available within Minitab.

Choose the data. Select and copy the data from spreadsheet on which you want to perform the normality test. 3. Paste the data in Minitab worksheet. Open Minitab and paste the data in Minitab worksheet. 4. Click "Stat". In the menu bar of Minitab, click on Stat. 5.

What Do t-Values Mean? Each type of t-test uses a procedure to boil all of your sample data down to one value, the t-value. The calculations compare your sample mean(s) to the null hypothesis and incorporates both the sample size and the variability in the data. A t-value of 0 indicates that the sample results exactly equal the null hypothesis.

To determine whether to reject the null hypothesis using the t-value, compare the t-value to the critical value. The critical value is t α/2, n-p-1, where α is the significance level, n is the number of observations in your sample, and p is the number of predictors. If the absolute value of the t-value is greater than the critical value ...

That probability allows us to determine how common or rare our F-value is under the assumption that the null hypothesis is true. If the probability is low enough, we can conclude that our data is inconsistent with the null hypothesis. The evidence in the sample data is strong enough to reject the null hypothesis for the entire population.

One-way ANOVA is a hypothesis test that evaluates two mutually exclusive statements about two or more population means. These two statements are called the null hypothesis and the alternative hypotheses. A hypothesis test uses sample data to determine whether to reject the null hypothesis. The null hypothesis (H 0) is that the group means are ...