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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. AP3.9 (page 702)

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 the following would be the most useful for making this comparison?
a. Back-to-back stem plots for A and B
b. A scatterplot of A versus B
c. Two dot plots 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 bar graphs for A and B drawn on the same scale

Short Answer

Expert verified

The correct option is (d) two relative frequency histograms of A and B drawn on the same rule.

Step by step solution

01

Given Information

We have to determine the comparison that is useful for the local newspapers distributions of SAT scores.

02

Simplification

Because the populations of both schools have varying numbers of students, the relative frequency histogram is used to standardize the number of individuals per school and make it more efficient for comparing and comprehending populations.

The distribution knowledge is far superior than frequency histograms and far superior to stem plots.

As a result, when you have a lot of data, stem and leaf plots aren't as informative. Because SAT scores are numerical and ordinal, a histogram would be far more useful and efficient.

Hence, the correct option is (d) two relative frequency histograms of A and B drawn on the same rule.

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Most popular questions from this chapter

A $96 %$ confidence interval for the proportion of the labor force that is unemployed in a certain city is $(0.07, 0.10) .$ Which of the following statements is true?

a. The probability is 0.96 that between $7 % a n d 10 %$ of the labor force is unemployed.

b. About $96 %$ of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.

c. In repeated samples of the same size, there is a $96 %$ chance that the sample proportion will fall between $0.07 a n d 0.10 .$

d. The true rate of unemployment in the labor force lies within this interval 96% of the time.

e. Between $7 % a n d 10 %$ of the labor force is unemployed 96% of the time.

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 respondent 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 should look at the data to

check Normality.

b. No; road rage scores on a scale from $0$ to $20$ 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.

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 $H_{0}$ : μsuburban=μcity versus a two-sided alternativ

The P-value for the test is $0.048$ . A correct conclusion is to

a. fail to reject $H_{0}$ because $0.048 < α = 0.05$ . There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

b. fail to reject $H_{0}$ because $0.048 < α = 0.05$ . There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

c. fail to reject $H_{0}$ because $0.048 < α = 0.05$ . There is convincing evidence that the average time spent on extracurricular activities by students in the suburban and city school districts is the same.

d. reject $H_{0}$ because $0.048 < α = 0.05$ . There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

e. reject $H_{0}$ because $0.048 < α = 0.05$ . There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

Broken crackers We don’t like to find broken crackers when we open the package. How can makers reduce breaking? One idea is to microwave the crackers for $30$ seconds right after baking them. Randomly assign $65$ newly baked crackers to the microwave and another $65$ to a control group that is not microwaved. After $1$ day, none of the microwave group were broken and $16$ of the control group were broken. Let $p_{1}$ be the true proportions of crackers like these that would break if baked in the microwave and $p_{2}$ be the true proportions of crackers like these that would break if not microwaved. Check if the conditions for calculating a confidence interval for $p_{1} - p_{2}$ met.

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?

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