Textbook Question
In Exercise 1, you rejected the claim that p=0.53. But this claim was true. What type of error is this?
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
1:54 minutesProblem 7.31
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.
Right-tailed test, α=0.02, n=63
Verified step by step guidance1
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 = 63 - 1.
Identify the level of significance (α) for the test. Here, α = 0.02, which corresponds to the probability of rejecting the null hypothesis when it is true.
Since this is a right-tailed test, the critical value corresponds to the t-score where the area to the right under the t-distribution curve equals α. Use a t-distribution table or statistical software to find the t-score for df = 62 and α = 0.02.
Define the rejection region. For a right-tailed test, the rejection region consists of all t-scores greater than the critical value found in the previous step.
Summarize the results: The critical value and rejection region are determined based on the t-distribution table or software output. The rejection region is t > critical value.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Critical Value
The 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 right-tailed t-test, the critical value is the point beyond which the null hypothesis is rejected, indicating that the observed data is statistically significant.
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Rejection Region
The rejection region is the set of values for the test statistic that leads to the rejection of the null hypothesis. In a right-tailed t-test, this region is located to the right of the critical value on the t-distribution curve. If the calculated test statistic falls within this region, it suggests that the sample provides sufficient evidence to reject the null hypothesis at the specified significance level.
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Guided course
09:56Step 4: State Conclusion
T-Test
A t-test is a statistical test used to compare the means of two groups or to compare a sample mean to a known value when the population standard deviation is unknown. It is particularly useful for small sample sizes (typically n < 30) and is based on the t-distribution. The type of t-test (one-sample, independent two-sample, or paired sample) depends on the data structure and research question.
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