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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 10: Q. 29 (page 626)

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 鈥淵es.鈥� Take $p_{M}$ and localid="1650271716184" $p_{F}$ be the proportions of all college males and females who worked last summer. We conjectured before seeing the data that men are more likely to work. The hypotheses to be tested are
(a) $H_{0} : p_{M} - p_{f} = 0$ versus $H_{a}; p_{M} - p_{F} 鈮� 0$
(b) $H_{0} : p_{M} - p_{F} = 0$ versus $H_{a} : p_{M} - p_{F} > 0$ .
(c) $H_{0} : p_{M} - p_{F} = 0$ versus $H_{a} : p_{M} - p_{F} < 0$
(d) $H_{0} : p_{M} - p_{F} > 0$ versus $H_{a} : p_{M} - p_{F} = 0$
(e) $H_{0} : p_{M} - p_{F} 鈮� 0$ versus $H_{a} : p_{M} - p_{F} = 0$

Short Answer

Expert verified

The tested hypothesis is option (b) $H_{0} : p_{M} - p_{F} = 0, H_{a} : p_{M} - p_{F} > 0 .$

Step by step solution

01

Given information

Male proportions in the college $= p_{M} = 484$

Female proportion in the college $= p_{F}$ $= 410$

To find the correct hypothesis.

02

Explanation

The equal sign is always used in the null hypothesis

$H_{0} : p_{M} - p_{F} = 0$

The alternative hypothesis contradicts the null hypothesis (according to the claim)

$H_{a} : p_{M} - p_{F} > 0$

Because of $p_{M} - p_{F} > 0$

Then, $p_{M} > p_{F}$

So it is option (b) $H_{0} : p_{M} - p_{F} = 0, H_{a} : p_{M} - p_{F} > 0 .$

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Most popular questions from this chapter

The level of cholesterol in the blood for all men aged $20$ to $34$ follows a Normal distribution with mean $188$ milligrams per deciliter (mg/dl) and a standard deviation $41$ mg/dl. For $14$ -year-old boys, blood cholesterol levels follow a Normal distribution with a mean $170$ mg/dl and a standard deviation of $30$ mg/dl.

(a) Let M $=$ the cholesterol level of a randomly selected $20$ to $34$ -year-old man and B =the cholesterol level of a randomly selected $14$ -year-old boy. Describe the shape, center, and spread of the distribution of $M - B$

(b) Find the probability that a randomly selected $14$ -year-old boy has higher cholesterol than a randomly selected man aged $20$ to $34$ . Show your work.

The correlation between the heights of fathers and the heights of their (grownup) sons is $r = 0.52$ , both measured in inches. If fathers鈥� heights were measured in feet and sons鈥� heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

(a) much smaller than 0.52.

(b) slightly smaller than 0.52.

(c) unchanged; equal to 0.52.

(d) slightly larger than 0.52.

(e) much larger than 0.52.

Men versus women The National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey interviewed a random sample of $1917$ people $21$ to $25$ years old. The sample contained $840$ men and $1077$ women. $^{49}$ The mean and standard deviation of scores on the NAEP's test of quantitative skills were ${\overset{炉}{x}}_{1} = 272.40$ and $s_{1} = 59.2$ for the men in the sample. For the women, the results were ${\overset{炉}{x}}_{2} = 274.73$ and $s_{2} = 57.5$ . Is the difference between the mean scores for men and women significant at the $1 %$ level? Give appropriate statistical evidence to justify your answer.

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 鈥淵es.鈥� The pooled sample proportion who worked last summer is about

(a) ${\overset{铃�}{p}}_{C} = 1.70$

(b) ${\hat{p}}_{C} = 0.89$

(c) ${\hat{p}}_{C} = 0.88$

(d) ${\hat{p}}_{C} = 0.85$

(e) ${\hat{p}}_{C} = 0.82$

44. Tropical flowers Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds.

Researchers believe that over time, the lengths of the flowers and the forms of the hummingbirds鈥� beaks have evolved to match each other. Here are data on the lengths in millimeters for random samples of two color varieties of the same species of flower on the island of Dominica:

(a) A Fathom dotplot of the data is shown below. Use the graph to answer these questions:

Are the centers of the two groups similar or different? Explain
Are the spreads of the two groups similar or different? Explain.

(b) Construct and interpret a 95% confidence interval for the difference in the mean lengths of these two varieties of flowers.
(c) Does the interval support the researchers鈥� belief that the two flower varieties have different average lengths? Explain.

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