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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. 9 (page 667)

School $A$ has $400$ students and School $B$ has $2700$ students. A local newspaper wants to compare the distributions of SAT scores for the two schools. Which of he following would be the most useful for making this comparison?
(a) Back-to-back stemplots for A and B
(b) A scatterplot of A versus B
(c) Dotplots for A and B drawn on the same scale
(d) Two relative frequency histograms of A and B drawn on the same scale
(e) Two frequency histograms for A and B drawn on the same scale

Short Answer

Expert verified

Two relative histograms of A and B drawn on the same scale.

Step by step solution

01

Given information

we have been given that A has $400$ students and B has $2700$ students.

02

Explanation

As we know that both populations have different number of the students.A frequency histogram makes it much more efficient at comapring populations and understanding their distribution and infinitely better.

It is very clear that when you have large amount of data plots are not useful.In these cases histogram would be better.

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Most popular questions from this chapter

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.

How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good indicator of decay. Lower strength means the fabric has decayed. For one part of the study, the researcher buried $10$ strips of polyester fabric in well-drained soil in the summer. The strips were randomly assigned to two groups: $5$ of them were buried for $2$ weeks and the other $5$ were buried for $16$ weeks. Here are the breaking strengths in pounds

Do the data give good evidence that polyester decays more in $16$ weeks than in $2$ weeks? Carry out an appropriate test to help answer this question .

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine’s manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean $27$ ounces and standard deviation $0.8$ ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean $17$ ounces and standard deviation $0.5$ ounces. To test the manufacturer’s claim, the restaurant manager measures the amount of liquid in a random sample of $25$ cups filled with the medium setting and a separate random sample of $20$ cups filled with the large setting. Let $x_{1} - x_{2}$ be the difference in the sample mean amount of liquid under the two settings (large – medium). What is the shape of the sampling distribution of ${\bar{x}}_{1} - {\bar{x}}_{2}$ . Why?

Quality control $(2.2, 5.3, 6.3)$ Many manufacturing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the production shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean $μ$ , with a standard deviation of $σ$ . For each question that follows, assume that the process is working properly.

(a) What's the probability that at least one of the next two sample means will fall more than $2 σ$ from the target mean $μ$ ? Show your work.

(b) What's the probability that the first sample mean that is greater than $μ + 2 σ$ is the one from the fourth sample taken?

(c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the $5$ most recent sample means. If at least $4$ of the $5$ fall outside the interval $(μ - σ, μ + σ)$ , they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.

Refer to Exercise $16$ .

(a) Carry out a significance test at the $α = 0.05$ level.

(b) Construct and interpret a $95 %$ confidence interval for the difference between the population proportions. Explain how the confidence interval is consistent with the results of the test in part (a).

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