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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. 64 (page 658)

Dropping out You have data from interviews with a random sample of students who failed to graduate from a particular college in $7$ years and also from a random sample of students who entered at the same time and did graduate. You will use these data to compare the percentages of students from rural backgrounds among dropouts and graduates.

Short Answer

Expert verified

Two proportion z-test.

Step by step solution

01

Given Information

Given in the question that,data from interviews with a random sample of students who failed to graduate from a particular college inyears and also from a random sample of students who entered at the same time and did graduate

02

Explanation

The $z$ - test for two sample proportions is a technique of the statistics that is check out if there is a difference in the proportions of two populations or not. Here, it is required to compare the percentage of students from rural background.

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Most popular questions from this chapter

A sample survey interviews SRSs of $500$ female college students and $550$ male college students. Each student is asked whether he or she worked for pay last summer. In all, $410$ of the women and $484$ of the men say “Yes.” The $95 %$ confidence interval for the difference $p_{M} - p_{F}$ in the proportions of college men and women who worked last summer is about

(a) $0.06 \pm 0.00095$

(b) $0.06 \pm 0.043 .$

(c) $0.06 \pm 0.036$

(d) $- 0.06 \pm 0.043$

(e) $- 0.06 \pm 0.036$

A study of road rage asked separate random samples of $596$ men and $523$ women about their behavior while driving. Based on their answers, each re-spondent was assigned a road rage score on a scale of $0$ to $20$ . Are the conditions for performing a two-sample t test satisfied?

a) Maybe; we have independent random samples, but we need to look at the data to check Normality.

(b) No; road rage scores in a range between $0$ and $20$ can’t be Normal.

(c) No; we don’t know the population standard deviations.

(d) Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.

(e) Yes; we have two independent random samples and large sample sizes.

National Park rangers keep data on the bears that inhabit their park. Below is a histogram of the weights of $143$ bears measured in a recent year.

Which statement below is correct?

(a) The median will lie in the interval ( $140, 180$ ), and the mean will lie in the interval ( $180, 220$ ).

(b) The median will lie in the interval ( $140, 180$ ), and the mean will lie in the interval ( $260, 300$ ).

(c) The median will lie in the interval ( $100, 140$ ), and the mean will lie in the interval ( $180, 220$ ).

(d) The mean will lie in the interval ( $140, 180$ ), and the median will lie in the interval ( $260, 300$ ).

(e) The mean will lie in the interval ( $100, 140$ ), and the median will lie in the interval ( $180, 200$ ).

A certain candy has different wrappers for various holidays. During Holiday $1$ the candy wrappers are $30 %$ silver, $30 %$ red, and $40 %$ pink. During Holiday $2$ the wrappers are $50 %$ silver and $50 %$ blue. Forty pieces of candy are randomly selected from the Holiday $1$ distribution, and $40$ pieces are randomly selected from the Holiday $2$ distribution. What are the expected value and standard deviation of the total number of silver wrappers?

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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