/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 77 For each of the following exampl... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 77

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 \(\alpha=.10\) b. A left-tailed test with \(\alpha=.01\) c. A right-tailed test with \(\alpha=.05\)

Short Answer

Expert verified
The rejection and acceptance regions depend on the type of test (two-tailed, left-tailed, or right-tailed) and the significance level. For a two-tailed test, the rejection regions are on both ends of the distribution and acceptance region in the middle. For a left-tailed test, the rejection region is on the left end of the distribution and acceptance region on the right. For a right-tailed test, the rejection region is on the right end of the distribution and the acceptance region on the left.

Step by step solution

01

Analyze the cases

There are three cases given in the exercise. The first one is a two-tailed test with alpha equal to 0.10. The second one is a left-tailed test with alpha equal to 0.01 and the third one is a right-tailed test with alpha equal to 0.05.
02

Locate the rejection and acceptance regions for the two-tailed test

For a two-tailed test, the rejection areas are located at both ends of the sampling distribution. Since \(\alpha=.10\) is given, split \(\alpha\) equally between the two tails. So, \(0.10/2 = 0.05\) for each tail. Find the z-scores that correspond to 0.05 in the left tail and 0.05 in the right tail using the z-score table or a statistical software tool. The area between these two z-scores is the acceptance region and outside of these is the rejection region.
03

Locate the rejection and acceptance regions for the left-tailed test

For a left-tailed test, the rejection region is located on the left end of the distribution. Since \(\alpha=.01\), find the z-score that corresponds to 0.01 on the z-table or statistical software. The area to the left of this z-score is the rejection region and area to the right is the acceptance region.
04

Locate the rejection and acceptance regions for the right-tailed test

For a right-tailed test, the rejection region is located on the right end of the distribution. Since, \(\alpha=.05\) is given, find the z-score that corresponds to 0.05 on the z-table or statistical software. The area to the right of this z-score is the rejection region and to the left is the acceptance region.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

food company is planning to market a new type of frozen yogurt. However, before marketing thit yogurt, the company wants to find what percentage of the people like it. The company's management has decided that it will market this yogurt only if at least \(35 \%\) of the people like it. The company's researcl department selected a random sample of 400 persons and asked th taste this yogurt. Of these 400 persons, 112 said they liked a. Testing at a \(2.5 \%\) significance level, can you conclude that the company should market this yogurt b. What will your decision be in part a if the probability of making a Type I error is zero? Explain Make the test of part a using the \(p\) -value approach.min

According to the U.S. Bureau of Labor Statistics, all workers in America who had a bachelor's degree and were employed earned an average of \(\$ 1038\) a week in \(2010 .\) A recent sample of 400 American workers who have a bachelor's degree showed that they earn an average of \(\$ 1060\) per week. Suppose that the population standard deviation of such earnings is \(\$ 160 .\) a. Find the \(p\) -value for the test of hypothesis with the alternative hypothesis that the current mean weekly earning of American workers who have a bachelor's degree is higher than \(\$ 1038 .\) Will you reject the null hypothesis at \(\alpha=.025 ?\) b. Test the hypothesis of part a using the critical-value approach and \(\alpha=.025\).

Which of the two hypotheses (null and alternative) is initially assumed to be true in a test of hypothesis?

Records in a three-county area show that in the last few years. Girl Scouts sold an average of \(47.93\) boxes of cookies per year per girl scout, with a population standard deviation of \(8.45\) boxes per year. Fifty randomly selected Girl Scouts from the region sold an average of \(46.54\) boxes this year. Scout leaders are concerned that the demand for Girl Scout cookies may have decreased A. Test at a \(10 \%\) significance level whether the average number of boxes of cookies sold by all Gir Scouts in the three-county area is lower than the historical average of \(47.92\) b. What will your decision be in part a if the probability of a Type I error is zero? Expl.

Consider \(H_{0}=\mu=20\) versus \(H_{1}: \mu<20 .\) A. What type of error would you make if the null hypothesis is actually false and you fail to reject it? b. What type of error would you make if the null hypothesis is actually true and you reject it?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.