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Chapter 9: Q. 58 (page 564)

Which of the following is not a condition for performing a significance test about an unknown population proportion p?

(a) The data should come from a random sample or randomized experiment.

(b) Individual measurements should be independent of one another.

(c) The population distribution should be approximately Normal, unless the sample size is large.

(d) Both np and n(1 - p) should be at least 10.

(e) If you are sampling without replacement from a finite population, then you should sample no more than 10% of the population.

Short Answer

Expert verified

(b) Individual measurements should be independent of one another.

Step by step solution

01

Given information

Significance test about an unknown population proportion p.

The population distribution should be normal unless the sample size is large.

02

Explanation

The procedure for the significance test is as follows:

State: What hypotheses do you want to test, and at what significance level?

Define any parameters you use.

Plan: Choose the appropriate inference method. Check conditions.

Do: If the conditions are met, perform calculations.

  • Compute the test statistic.
  • Find the P-value.

Conclude: Interpret the results of your test in the context of the problem.

From the above statement, we conclude that the option b individual measurements should be independent of one another.

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Most popular questions from this chapter

Calculations and conclusions Refer to Exercise R9.1. Find the standardized test statistic and P-value in each setting, and make an appropriate conclusion.

Better parking A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school’s students approved of the parking that was provided. After the change, the principal surveys an SRS of students at the school. She would like to perform a test of H0:p=0.37Ha:p>0.37where p is the true proportion of students at school who are satisfied with the parking

situation after the change.

a. The power of the test to detect that p=0.45 based on a random sample of 200 students and a significance level of α=0.05 is 0.75 Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

Significance tests A test of H0:p=0.65 against Ha:p<0.65

based on a sample of size 400 yields the standardized test statistic z=−1.78 .

a. Find and interpret the P-value.

b. What conclusion would you make at the α=0.10 significance level? Would

your conclusion change if you used α=0.05 instead? Explain your reasoning.

c. Determine the value of p⏜= the sample proportion of successes.

Jump around Refer to Exercise 78.

a. Construct and interpret a 90% confidence interval for the true mean vertical jump μ(in inches) of the students at Haley, Jeff, and Nathan’s school. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 78

Do you Tweet? The Pew Internet and American Life Project asked a random sample of U.S. adults, “Do you ever … use Twitter or another service to share updates about yourself or to see updates about others?” According to Pew, the resulting 95% confidence interval is (0.123, 0.177).11 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they use Twitter or another service to share updates differs from 0.17? Explain your reasoning.
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