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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 10: Q. AP3.26 (page 704)

A large university is considering the establishment of a schoolwide recycling program. To gauge interest in the program by means of a questionnaire, the university takes separate random samples of undergraduate students, graduate students, faculty, and staff. This is an example of what type of sampling design?
a. Simple random sample
b. Stratified random sample
c. Convenience sample
d. Cluster sample
e. Randomized block design

Short Answer

Expert verified

The correct option is - (b) stratified random sample .

Step by step solution

01

Given Information

We are given random samples of undergraduate students, graduate students , faculty and staff . We need to find out this example falls under which category .

02

Explanation

This will be classified as stratified random sample because the overall population is divided into strata (sub populations based on a variable) : undergraduate students, graduate students, faculty, and staff.

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Most popular questions from this chapter

Drive-thru or go inside? Many people think it’s faster to order at the drive-thru than to order inside at fast-food restaurants. To find out, Patrick and William used a random number generator to select $10$ times over a $2 ‐$ week period to visit a local Dunkin’ Donuts restaurant. At each of these times, one boy ordered an iced coffee at the drive-thru and the other ordered an iced coffee at the counter inside. A coin flip determined who went inside and who went to the drive-thru. The table shows the times, in seconds, that it took for each boy to receive his iced coffee after he placed the order.

Do these data provide convincing evidence at the $α = 0.05$ level of a difference in the true mean service time inside and at the drive-thru for this Dunkin’ Donuts restaurant?

Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C. area is $0.45$ . In a simple random sample of $250$ people who work in Washington, about how far do you expect the sample proportion to be from the true proportion?

a. $0.4975$

b. $0.2475$

c. $0.0315$

d. $0.0009$

e. $0$

Researchers want to evaluate the effect of a natural product on reducing blood pressure. They plan to carry out a randomized experiment to compare the mean reduction in blood pressure of a treatment (natural product) group and a placebo group. Then they will use the data to perform a test of $H_{0} : μ_{T} - μ_{P} = 0$ versus $H_{a} : μ_{T} - μ_{P} > 0$ , where $μ_{T}$ = the true mean reduction in blood pressure when taking the natural product and μP = the true mean reduction in blood pressure when taking a placebo for subjects like the ones in the experiment. The researchers would like to detect whether the natural product reduces blood pressure by at least $7$ points more, on average, than the placebo. If groups of size $50$ are used in the experiment, a twosample t test using $α = 0.01$ will have a power of $80 %$ to detect a $7$ -point difference in mean blood pressure reduction. If the researchers want to be able to detect a $5$ -point difference instead, then the power of the test

a. would be less than $80 %$ .

b. would be greater than $80 %$ .

c. would still be $80 %$ .

d. could be either less than or greater than $80 %$ .

e. would vary depending on the standard deviation of the data

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of $H_{0} : μ_{s u b u r b a n} = μ_{c i t y}$ versus a two-sided alternative. Which is the correct standardized test statistic ?

(a) $z = \frac{(6 - 5) - 0}{\sqrt{\frac{3}{60} + \frac{2}{40}}}$

(b) $z = \frac{(6 - 5) - 0}{\sqrt{\frac{3^{2}}{60} + \frac{2^{2}}{40}}}$

(c) role="math" localid="1654192807425" $t = \frac{(6 - 5) - 0}{\frac{3}{\sqrt{60}} + \frac{2}{\sqrt{40}}}$

(d) $t = \frac{(6 - 5) - 0}{\sqrt{\frac{3}{60} + \frac{2}{40}}}$

(e) $t = \frac{(6 - 5) - 0}{\sqrt{\frac{3^{2}}{60} + \frac{2^{2}}{40}}}$

A random sample of $200$ New York State voters included $88$ Republicans, while a random sample of $300$ California voters produced $141$ Republicans. Which of the following represents the $95 %$ confidence interval for the true difference in the proportion of Republicans in New York State and California?

a. $(0.44 - 0.47) \pm 1.96 ((0.44) (0.56) + (0.47) (0.53) 200 + 300)$

b. $(0.44 - 0.47) \pm 1.96 ((0.44) (0.56) 200 + (0.47) (0.53) 300)$

c. ( $0.44 - 0.47) \pm 1.96 (0.44) (0.56) 200 + (0.47) (0.53) 300$

d. $(0.44 - 0.47) \pm 1.96 (0.44) (0.56) + (0.47) (0.53) 200 + 300$

e. $(0.44 - 0.47) \pm 1.96 (0.45) (0.55) 200 + (0.45) (0.55) 300$

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