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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

Chapter 10: Q. 62 (page 658)

Driving too fast 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 of 1 (no problem at all) to $5$ (very severe problem). Do speeding drivers get a higher average rating than noisy neighbors?

Short Answer

Expert verified

The appropriate procedure is Two sample tests.

Step by step solution

01

Given Information

How do people see speed in comparison to other aggravating behaviors? An unusually large group of adults was asked to score a variety of practices on a scale of I (no problem at all) to $5$ (very serious problem) (extremely serious issue). Whether or whether speeding drivers receive a higher typical rating than their noisy neighbours.

02

Explanation

An independent two-sample test determines if the mean difference between two sets of observations is equal to, greater than, or less than $0$ . To check the behavior, two different groups of observations were studied in this test process.

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Most popular questions from this chapter

Binge drinking Who is more likely to binge drink— male or female college students? The Harvard School of Public Health surveys random samples of male and female undergraduates at four-year colleges and universities about whether they have engaged in binge drinking.

(a) Is this a problem with comparing means or comparing proportions? Explain.

(b) What type of study design is being used to produce data?

A better drug? In a pilot study, a company's new cholesterol-reducing drug outperforms the currently available drug. If the data provide convincing

evidence that the mean cholesterol reduction with the new drug is more than 10 milligrams per deciliter of blood (mg/dl) greater than with the current drug, the company will begin the expensive process of mass-producing the new drug. For the 14 subjects who were assigned at random to the current drug, the mean cholesterol reduction was $54.1 mg / dl$ with a standard deviation of $11.93 m g / d l .$ For the 15 subjects who were randomly assigned to the new drug, the mean cholesterol reduction was $68.7 mg / dl$ with a standard deviation of $13.3 m g / d l .$ Graphs of the data reveal no outliers or strong skewness.

(a) Carry out an appropriate significance test. What conclusion would you draw? (Note that the null hypothesis is not $H_{0 : μ_{1} - μ_{2}} = 0_{-})$

(b) Based on your conclusion in part (a), could you have made a Type I error or a Type Il error? Justify your answer.

A beef rancher randomly sampled $42$ cattle from her large herd to obtain a $95 %$ confidence interval to estimate the mean weight of the cows in the herd. The interval obtained was $(1010, 1321)$ . If the rancher had used a $98 %$ confidence interval instead, the interval would have been

(a) wider and would have less precision than the original estimate.

(b) wider and would have more precision than the original estimate.

(c) wider and would have the same precision as the original estimate.

(d) narrower and would have less precision than the original estimate.

(e) narrower and would have more precision than the original estimate.

Preventing drowning Drowning in bathtubs is a major cause of death in children less than 5 years 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.

Do drivers reduce excessive speed when they encounter police radar? Researchers studied the behavior of a sample of drivers on a rural interstate highway in Maryland where the speed limit was $55$ miles per hour. They measured the speed with an electronic device hidden in the pavement and, to eliminate large trucks, considered only vehicles less than $20$ feet long. During some time periods (determined at random), police radar was set up at the measurement location. Here are some of the data.

$\begin{array}{lcc} Number of vehicles & Number over 65 mph \\ No radar & 12, 931 & 5, 690 \\ Radar & 3, 285 & 1, 051 \end{array}$

(a) The researchers chose a rural highway so that cars would be separated rather than in clusters because some cars might slow when they see other cars slowing. Explain why this is important.

(b) Does the proportion of speeding drivers differ significantly when the radar is being used and when it isn’t? Use information from the Minitab computer output below to support your answer.

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