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Chapter 8: Q5 (page 371)

Identifying H0 and H1 . In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Online Data Claim: Most adults would erase all of their personal information online if they could. A GFI Software survey of 565 randomly selected adults showed that 59% of them would erase all of their personal information online if they could.

Short Answer

Expert verified

a. The original claim in symbolic form is written in the following manner:

p>0.5

b. Null hypothesis: The proportion of adults who would erase all of their personal information online if they could is equal to 0.5.

Alternative hypothesis: The proportion of adults who would erase all of their personal information online if they could is greater than 0.5.

Step by step solution

01

Given information

Out of 565 randomly selected adults, 59% would erase all of their personal information online if they could.

02

Identify the original claim

a.

It is claimed that most adults would erase all of their personal information online if they could; this suggests that the original claim should be that the proportion of adults who would erase all of their personal information online if they could is greater than 50% or 0.5.

Symbolically, the claim would be p>0.5, where p is the proportion of adults who would erase all of their personal information online if they could.

03

Hypotheses

b.

Null hypothesis: The proportion of adults who would erase all of their personal information online if they could is equal to 0.5.

H0:p=0.5

Alternative hypothesis: The proportion of adults who would erase all of their personal information online if they could is greater than 0.5.

H1:p>0.5

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Most popular questions from this chapter

The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analysed with a formal hypothesis test with the alternative hypothesis of p>0.5, which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer: 0.999, 0.5, 0.95, 0.05, 0.01, and 0.001? Why?

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Course Evaluations Data Set 17 “Course Evaluations” in Appendix B includes data from student evaluations of courses. The summary statistics are n = 93, x = 3.91, s = 0.53. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.00.

Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Survey Return Rate In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 5000 subjects randomly selected from an online group involved with ears. 717 surveys were returned. Use a 0.01 significance level to test the claim that the return rate is less than 15%.

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Speed Dating Data Set 18 “Speed Dating” in Appendix B includes “attractive” ratings of male dates made by the female dates. The summary statistics are n = 199, x = 6.19, s = 1.99. Use a 0.01 significance level to test the claim that the population mean of such ratings is less than 7.00.

Critical Values. In Exercises 21–24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

Exercise 17
See all solutions

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