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Chapter 10: Q. 74. (page 672)

Stop doing homework! (4.3)Researchers in Spain interviewed 772513-year-olds about their homework habits—how much time they spent per night on homework and whether they got help from their parents or not—and then had them take a test with 24math questions and 24science questions. They found that students who spent between 90and 100minutes on homework did only a little better on the test than those who spent 60to 70minutes on homework. Beyond 100minutes, students who spent more time did worse than those who spent less time. The researchers concluded that 60to 70minutes per night is the optimum time for students to spend on homework.32 Is it appropriate to conclude that students who reduce their homework time from 120minutes to 70minutes will likely improve their performance on tests such as those used in this study? Why or why not? independent random samples from two populations of interest or from two groups in a randomized experiment, use two-sample t procedures for μ1−μ23051526=0.200=20.0%μ1-μ2

Short Answer

Expert verified

The required answer is No

Step by step solution

01

Explanation

In the previous exercise, we concluded that there was a link between homework time and test performance, such as those used in the study, because homework times longer than 100minutes tend to correspond with poor test results.

However, association does not imply causation, which means that reducing homework time does not always result in better test results.

02

For example

It is possible that people with long homework times have learning difficulties, and that reducing their homework time will worsen their test results.

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Most popular questions from this chapter

On your mark In track, sprinters typically use starting blocks because they think it will help them run a faster race. To test this belief, an experiment was designed where each sprinter on a track team ran a 50-meter dash two times, once using starting blocks and once with a standing start. The order of the two different types of starts was determined at random for each sprinter. The times (in seconds) for 8 different sprinters are shown in the table.

a. Make a dotplot of the difference (Standing - Blocks) in 50-meter run time for each sprinter. What does the graph suggest about whether starting blocks are helpful?

b. Calculate the mean difference and the standard deviation of the differences. Explain why the mean difference gives some evidence that starting blocks are helpful.

c. Do the data provide convincing evidence that sprinters like these run a faster race when using starting blocks, on average?

d. Construct and interpret a 90%confidence interval for the true mean difference. Explain how the confidence interval gives more information than the test in part (b).

Two samples or paired data? In each of the following settings, decide whether you should use two-sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference. Explain your choice.

a. To compare the average weight gain of pigs fed two different diets, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which pig in each pair got Diet A and which got Diet B.

b. Separate random samples of male and female college professors are taken. We wish to compare the average salaries of male and female teachers.

c. To test the effects of a new fertilizer, 100 plots are treated with the new fertilizer, and 100 plots are treated with another fertilizer. A computer’s random number generator is used to determine which plots get which fertilizer.

Coaching and SAT scores What we really want to know is whether coached students improve more than uncoached students, on average, and whether any advantage is large enough to be worth paying for. Use the information above to answer these questions:

a. How much more do coached students gain, on average, compared to uncoached students? Construct and interpret a 99%confidence interval.

b. Does the interval in part (a) give convincing evidence that coached students gain more, on average, than uncoached students? Explain your answer.

c. Based on your work, what is your opinion: Do you think coaching courses are worth paying for?

Which inference method?

a. Drowning in bathtubs is a major cause of death in children less than5years old. A random sample of parents was asked many questions related to bathtub safety. Overall,85%of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of young children who use baby bathtubs.

b. How seriously do people view speeding in comparison with other annoying behaviors? A large random sample of adults was asked to rate a number of behaviors on a scale of1(no problem at all) to5(very severe problem). Do speeding drivers get a higher average rating than noisy neighbors?

c. You have data from interviews with a random sample of students who failed to graduate from a particular college in7years and also from a random sample of students who entered at the same time and did graduate within7years. You will use these data to estimate the difference in the percent's of students from rural backgrounds among dropouts and graduates.

d. Do experienced computer-game players earn higher scores when they play with someone present to cheer them on or when they play alone? Fifty teenagers with experience playing a particular computer game have volunteered for a study. We randomly assign25 of them to play the game alone and the other25to play the game with a supporter present. Each player’s score is recorded.

Does music help or hinder memory? Many students at Matt’s school claim they can think more clearly while listening to their favorite kind of music. Matt believes that music interferes with thinking clearly. To find out which is true, Matt recruits 84 volunteers and randomly assigns them to two groups. The “Music” group listens to their favorite music while playing a “match the animals” memory game. The “No Music” group plays the same game in silence. Here are some descriptive statistics for the number of turns it took

the subjects in each group to complete the game (fewer turns indicate better performance):

Matt wants to know if listening to music affects the average number of turns required to finish the memory game for students like these.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.
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