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Chapter 10: Q. 42 (page 666)

For their final project, a group of AP庐 Statistics students wanted to compare the texting habits of males and females. They asked a random sample of students from their school to record the number of text messages sent and received over a 2-day period. Here are their data:

Let 渭1=the true mean number of texts sent by male students at the school and 渭2=the true mean number of texts sent by female students at the school. Check if the conditions for calculating a confidence interval for 渭1-渭2 are met.

Short Answer

Expert verified

Females group text more than males.

Step by step solution

01

Step 1. Given information

Given:

02

Step 2. Calculation

Let鈥檚 take given table and find out its sum first:

X炉M=鈭�XMn=9367=133.71X炉F=鈭�XFn=20527=294.14

From the above ratio values of males and females, the mean value of female group is more than male group that鈥檚 why the female groups text more.

Hence, females group text more than males.

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Most popular questions from this chapter

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 H0:渭T鈭�渭P=0versus Ha:渭T鈭�渭P>0, where 渭T= the true mean reduction in blood pressure when taking the natural product and 渭P = 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 7points more, on average, than the placebo. If groups of size 50are used in the experiment, a twosample t test using 伪=0.01will 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 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%and10% 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 0.07and0.10.

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

e. Between 7%and10%of the labor force is unemployed 96% of the time.

Suppose the probability that a softball player gets a hit in any single at-bat is 0.300. Assuming that her chance of getting a hit on a particular time at bat is independent of her other times at bat, what is the probability that she will not get a hit until her fourth time at bat in a game?

a.(43)(0.3)1(0.7)33051526=0.200=20.0%43(0.3)1(0.7)3

b.(43)(0.3)3(0.7)13051526=0.200=20.0%43(0.3)3(0.7)1

C.(41)(0.3)3(0.7)13051526=0.200=20.0%41(0.3)3(0.7)1

d.(0.3)3(0.7)13051526=0.200=20.0%(0.3)3(0.7)1

e.(0.3)1(0.7)33051526=0.200=20.0%(0.3)1(0.7)3

On your mark In track, sprinters typically use starting blocks because they think it will help them run a faster race. To test this belief, an experiment was designed where each sprinter on a track team ran a 50-meter dash two times, once using starting blocks and once with a standing start. The order of the two different types of starts was determined at random for each sprinter. The times (in seconds) for 8 different sprinters are shown in the table.

a. Make a dotplot of the difference (Standing - Blocks) in 50-meter run time for each sprinter. What does the graph suggest about whether starting blocks are helpful?

b. Calculate the mean difference and the standard deviation of the differences. Explain why the mean difference gives some evidence that starting blocks are helpful.

c. Do the data provide convincing evidence that sprinters like these run a faster race when using starting blocks, on average?

d. Construct and interpret a 90%confidence interval for the true mean difference. Explain how the confidence interval gives more information than the test in part (b).

A random sample of 200New York State voters included 88Republicans, while a random sample of 300California voters produced141Republicans. 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鈭�0.47)卤1.96((0.44)(0.56)+(0.47)(0.53)200+300)

b. (0.44鈭�0.47)卤1.96((0.44)(0.56)200+(0.47)(0.53)300)

c. (0.44鈭�0.47)卤1.96(0.44)(0.56)200+(0.47)(0.53)300

d. (0.44鈭�0.47)卤1.96(0.44)(0.56)+(0.47)(0.53)200+300

e. (0.44鈭�0.47)卤1.96(0.45)(0.55)200+(0.45)(0.55)300
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