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Chapter 9: Q.16 (page 547)
Asked to explain the meaning of “statistically significant at the A 0.05 level,” a
student says, “This means that the probability that the null hypothesis is true is less than 0.05.” Is this explanation correct? Why or why not?
The explanation is incorrect
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During the winter months, the temperatures at the Colorado cabin owned by the Starnes family can stay well below freezing (32°F or 0°C) for weeks at a time. To prevent the pipes from freezing, Mrs Starnes sets the thermostat at 50°F. The manufacturer claims that the thermostat allows variation in-home temperature of S 3°F. Mrs Starnes suspects that the manufacturer is overstating how well the thermostat works.
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.
Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if 12% of the students at his large public high school are left-handed. Simon chooses an SRS of 100 students and records whether each student is right- or left-handed.
Taking stock An investor with a stock portfolio worth several hundred thousand dollars sued his broker due to the low returns he got from the portfolio at a time when the stock market did well overall. The investor’s lawyer wants to compare the broker’s performance against the market as a whole. He collects data on the broker’s returns for a random sample ofweeks. Over the -year period that the broker has managed portfolios, stocks in the Standard & Poor’s index gained an average of per month. The Minitab output below displays descriptive statistics for these data, along
with the results of a significance test.
(a) Determine whether there are any outliers. Show your work.
(b) Interpret the P-value in context.
(c) Do these data give convincing evidence to support the lawyer’s case? Carry out a test to help you answer this question.
Would the hypothesis that be rejected at the level in favor of a two-sided alternative? Justify your answer.
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