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Chapter 9: Q.1.2 Intercepts; Symmetry; Graphing Key Equations (page 532)

As part of its 2010 census marketing campaign, the U.S. Census Bureau advertised

“10 questions, 10 minutes—that’s all it takes.” On the census form itself, we read, “The

U.S. Census Bureau estimates that, for the average household, this form will take

about 10 minutes to complete, including the time for reviewing the instructions and

answers.” We suspect that the actual time it takes to complete the form may be longer

than advertised.

Short Answer

Expert verified

The boundary of interest is the real population mean measure of time expected to finish the type of census.

Step by step solution

01

introduction

Given,

The U.S. Census Bureau estimates that, for the average household, this form will take

about 10minutes to complete, including the time for reviewing the instructions and

answers.

02

explanation

The boundary of interest is the real population mean measure of time expected to finish the type of census.

mean = 10

The null hypothesis is,H0:μ=10

The alternate hypothesis is Ha:μ<10

The test is left tailed.

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Most popular questions from this chapter

Stating hypotheses State the appropriate null and alternative hypotheses in each of the following cases.

(a) The average height of 18-year-old American women is 64.2inches. You wonder whether the mean height of this year's female graduates from a large local high school (over 3000students) differs from the national average. You measure an SRS of 48female graduates and find that X=63.1inches.

(b) Mr. Starnes believes that less than 75%of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of students at the school to help Mr. Starnes test his claim.

- Check conditions for carrying out a test about a population proportion or mean.

- Interpret P-values in context.

According to the Web site sleepdeprivation.com, 85% of teens are getting less than

eight hours of sleep a night. Jannie wonders whether this result holds in her large high school. She asks an SRS of 100 students at the school how much sleep they get on a typical night. In all, 75 of the responders said less than 8 hours.

One-sided test Suppose you carry out a significance test of H0:μ=5versus Ha:μ>5based on a sample of size n=20and obtain t=1.81.

(a) Find the P-value for this test using (i) Table Band (ii) your calculator. What conclusion would you draw at the 5%significance level? At the 1%significance level?

(b) Redo part (a) using an alternative hypothesis ofHa:μ≠5.

Cash to find work? (5.2) Will cash bonuses speed the return to work of unemployed people? The Illinois Department of Employment Security designed an experiment to find out. The subjects were 10,065 people aged 20 to 54 who were filing claims for

unemployment insurance. Some were offered \(500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer \)500 for hiring them. A control group got neither kind of bonus.

(a) Describe a completely randomized design for this experiment.

(b) How will you label the subjects for random assignment? Use Table D at line 127 to choose the first 3 subjects for the first treatment.

(c) Explain the purpose of a control group in this setting.

The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25right-handed students to turn a knob (with their right hands) that moved an indicator. There were two identical instruments, one with a right-hand thread (the knob turns clockwise) and the other with a left-hand thread (the knob must be turned counterclockwise). Each of the 25students used both instruments in a random order. The following table gives the times in seconds each subject took to move the indicator a fixed distance:

(a) Explain why it was important to randomly assign the order in which each subject used the two knobs.

(b) The project designers hoped to show that right-handed people find right-hand threads easier to use. Carry out a significance test at the 5%significance level to investigate this claim
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