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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2:15 minutes

Problem 7.RE.33

Textbook Question

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.

Left-tailed test, α=0.05, n=15

Verified step by step guidance

Determine the degrees of freedom (df) for the t-test. The formula for degrees of freedom is df = n - 1, where n is the sample size. In this case, df = 15 - 1.

Identify the level of significance (α). For this problem, α = 0.05, which represents the probability of rejecting the null hypothesis when it is true.

Since this is a left-tailed test, the critical value corresponds to the t-score where the cumulative probability to the left of the t-score equals α. Use a t-distribution table or statistical software to find the critical t-value for df = 14 and α = 0.05.

Define the rejection region. For a left-tailed test, the rejection region is t < critical value. This means any t-score less than the critical value will lead to rejecting the null hypothesis.

Summarize the critical value and rejection region. Clearly state the critical t-value and the corresponding rejection region based on the calculations or table lookup.

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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 threshold that determines the boundary for rejecting the null hypothesis in hypothesis testing. It is derived from the chosen significance level (α) and the distribution of the test statistic. For a left-tailed t-test, the critical value is the point on the t-distribution that corresponds to the cumulative probability of α, indicating the cutoff for the rejection region.

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 left-tailed test, this region is located to the left of the critical value. If the calculated test statistic falls within this region, it suggests that the sample provides sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

t-Test

A t-test is a statistical test used to determine if there is a significant difference between the means of two groups, particularly when the sample size is small and the population standard deviation is unknown. The test uses the t-distribution, which accounts for the sample size and variability. In this case, a left-tailed t-test is employed to assess whether the sample mean is significantly less than a hypothesized population mean.

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In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.Left-tailed test, α=0.05, n=15

Key Concepts

Critical Value

Rejection Region

t-Test

Watch next

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.

Left-tailed test, α=0.05, n=15