Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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2:35 minutes

Problem 7.4.5

Textbook Question

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.
Right-tailed test, α=0.05, n=23

Verified step by step guidance

Step 1: Identify the degrees of freedom (df) for the t-test. The degrees of freedom are calculated as df = n - 1, where n is the sample size. For this problem, df = 23 - 1.

Step 2: Recognize that this is a right-tailed t-test. This means the rejection region will be in the upper tail of the t-distribution.

Step 3: Use the level of significance (α = 0.05) and the degrees of freedom (df = 22) to find the critical value from a t-distribution table or statistical software. Look up the t-value corresponding to a cumulative probability of 1 - α = 0.95 for df = 22.

Step 4: Define the rejection region. For a right-tailed test, the rejection region consists of all t-values greater than the critical value found in Step 3.

Step 5: Summarize the results. The critical value and rejection region are now determined, and these will be used to decide whether to reject the null hypothesis in the context of the t-test.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Critical Value

A critical value is a point on the scale of the test statistic that separates the region where the null hypothesis is rejected from the region where it is not rejected. In hypothesis testing, critical values are determined based on the significance level (alpha) and the distribution of the test statistic. For a right-tailed t-test, the critical value corresponds to the point where the cumulative probability equals 1 - alpha.

Rejection Region

The rejection region is the range of values for the test statistic that leads to the rejection of the null hypothesis. In a right-tailed test, this region is located to the right of the critical value. If the calculated test statistic falls within this region, it indicates that the observed data is sufficiently unlikely under the null hypothesis, prompting its rejection.

T-Test

A t-test is a statistical test used to determine if there is a significant difference between the means of two groups, or between a sample mean and a known value. It is particularly useful when the sample size is small (typically n < 30) and the population standard deviation is unknown. The t-test uses the t-distribution, which accounts for the additional uncertainty introduced by estimating the population standard deviation from the sample.

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In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.Right-tailed test, α=0.05, n=23

Key Concepts

Critical Value

Rejection Region

T-Test

Watch next

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.
Right-tailed test, α=0.05, n=23