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Chapter 9: Problem 78

For each of the following examples of tests of hypothesis about the population proportion, show the rejection and nonrejection regions on the graph of the sampling distribution of the sample proportion. a. A two-tailed test with \(\alpha=.05\) b. A left-tailed test with \(\alpha=.02\) c. A right-tailed test with \(\alpha=.025\)

Short Answer

Expert verified
The rejection regions vary according to whether the test is two-tailed, left-tailed, or right-tailed and by the value of \(\alpha\). For a two-tailed test with \(\alpha=.05\), rejection regions are present in both tails accounting for 5% total. For a left-tailed test with \(\alpha=.02\), 2% on the left tail is the rejection region. For a right-tailed test with \(\alpha=.025\), 2.5% on the right tail is the rejection region.

Step by step solution

01

Identify the Type of Test and Draw the Distribution

Identify whether the test is two-tailed, left-tailed, or right-tailed and proceed to draw the normal distribution curve accordingly. The center of the curve represents the hypothesized proportion.
02

Determine the Rejection and Non-rejection Regions for Two-tailed Test

For a two-tailed test where \(\alpha = 0.05\), this represents a 5% chance of wrongly rejecting the null hypothesis, therefore, the rejection regions are 2.5% on both tails, while the rest 95% in the middle is the non-rejection region.
03

Determine the Rejection and Non-rejection Regions for Left-tailed Test

For a left-tailed test where \(\alpha = 0.02\), this represents a 2% chance of wrongly rejecting the null hypothesis on the left side. Therefore, the left tail has the rejection region, while the rest (98%) is the non-rejection region.
04

Determine the Rejection and Non-rejection Regions for Right-tailed Test

For a right-tailed test where \(\alpha = 0.025\), this indicates a 2.5% chance of wrongly rejecting the null hypothesis on the right side. Therefore, the right tail has the rejection region, while the rest (97.5%) is the non-rejection region.

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Most popular questions from this chapter

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