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Chapter 7: Q64E (page 424)

Suppose a random sample of 100 observations from a binomial population gives a value of \(\hat p = .63\) and you wish to test the null hypothesis that the population parameter p is equal to .70 against the alternative hypothesis that p is less than .70.

a. Noting that\(\hat p = .63\) what does your intuition tell you? Does the value of \(\hat p\) appear to contradict the null hypothesis?

Short Answer

Expert verified
  1. The population parameter may be less than .70 as the sample proportion comes out to be less than 0.70.

Step by step solution

01

Given Information

The hypothesis are given by

\(\begin{aligned}{H_0}:p = .70\\{H_a}:p < .70\end{aligned}\)

The sample size is 100

02

Sample size

A group selected from a population is a sample. Samples are taken from the population. Sample size tell us how many people from the population are included in the sample.

03

Step 3:

The difference is .70. The sample mean is .63. The intuition tells us that the value of .70 is not necessarily wrong; it is possible that the true mean is actually below 0.70.

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Most popular questions from this chapter

Americans’ favorite sport. The Harris Poll (December 2013) conducted an online survey of American adults to determine their favorite sport. Your friend believes professional (National Football League [NFL]) football—with revenue of about $13 billion per year—is the favorite sport for 40% of American adults. Specify the null and alternative hypotheses for testing this belief. Be sure to identify the parameter of interest.

In a test of H0:μ=100againstHa:μ>100, the sample data yielded the test statistic z = 2.17. Find and interpret the p-value for the test.

Refer to Exercise 6.44 (p. 356), in which 50 consumers taste-tested a new snack food. Their responses (where 0 = do not like; 1 = like; 2 = indifferent) are reproduced below

  1. Test \({H_0}:p = .5\) against \({H_0}:p > .5\), where p is the proportion of customers who do not like the snack food. Use \(\alpha = 0.10\).
    1 0 0 1 2 0 1 1 0 0 0 1 0 2 0 2 2 0 0 1 1 0 0 0 0 1 0 2 0 0 0 1 0 0 1 0 0 1 0 1 0 2 0 0 1 1 0 0 0 1

Consider the test of H0:μ=7. For each of the following, find the p-value of the test:

a.Ha:μ>7 ; z=1.20

b.Ha:μ<7 ; z=-1.20

c.Ha:μ≠7 ; z=1.20

The opinions of employees at Asia-Pacific firms regarding fraud, bribery, and corruption in the workplace were elicited in the 2015 AsiaPacific (APAC) Fraud Survey. Interviews were conducted with a sample 1,508 employees of large APAC companies. One question concerned whether or not the employee’s company had implemented a “whistle-blower” hotline—that is, a phone number that an employee can call to report fraud or other types of misconduct without fear of retribution. The 2015 survey found that 680 of the 1,508 respondents’ companies had not implemented a whistle-blower hotline. In comparison, 436 of the 681 respondents in the 2013 survey reported their companies had not implemented a whistle-blower hotline.

a. TestH0:p=.5 against Ha:p<.5using data from the 2015 survey and α=.05Give a practical interpretation of the results.

b. Test H0:p=.5against Ha:p>.5using data from the 2013 survey andα=.05 Give a practical interpretation of the results.
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