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Chapter 10: Q. 41 (page 666)

How many pairs of shoes do teenagers have? To find out, a group of AP庐 Statistics students conducted a survey. They selected a random sample of 20female students and a separate random sample of 20male students from their school. Then they recorded the number of pairs of shoes that each student reported having. Here are their data:

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

Short Answer

Expert verified

Females and males groups have 30.5and 11.6pairs of shoes respectively.

Step by step solution

01

Step 1. Given information

Given:

02

Step 2. Concept used

The Mean formula: x炉=鈭�Xn

where,

Sum of all data values:鈭�X

Number of data values: n

03

Step 3. Calculation

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

Now, the pairs of shoes having by teenagers is calculated by calculating the mean:

X炉M=鈭�232n=23220=11.6X炉F=鈭�607n=23220=30.5

Hence, females and males groups have 30.5and 11.6pairs of shoes respectively.

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Most popular questions from this chapter

Have a ball! Can students throw a baseball farther than a softball? To find out, researchers conducted a study involving 24randomly selected students from a large high school. After warming up, each student threw a baseball as far as he or she could and threw a softball as far as he she could, in a random order. The distance in yards for each throw was recorded. Here are the data, along with the difference (Baseball 鈥� Softball) in distance thrown, for each student:

a. Explain why these are paired data.

b. A boxplot of the differences is shown. Explain how the graph gives some evidence that students like these can throw a baseball farther than a softball.

c. State appropriate hypotheses for performing a test about the true mean difference. Be sure to define any parameter(s) you use.

d. Explain why the Normal/Large Sample condition is not met in this case. The mean difference (Baseball鈭扴oftball) in distance thrown for these 24students is xdiff = 6.54yards. Is this a surprisingly large result if the null hypothesis is true? To find out, we can perform a simulation assuming that students have the same ability to throw a baseball and a softball. For each student, write the two distances thrown on different note cards. Shuffle the two cards and designate one distance to baseball and one distance to softball. Then subtract the two distances (Baseball鈭扴oftball) . Do this for all the students and find the simulated mean difference. Repeat many times. Here are the results of 100trials of this simulation

e. Use the results of the simulation to estimate the P-value. What conclusion would you draw ?

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Do these data give convincing evidence of a difference in the population means at the 伪=0.103051526=0.200=20.0%伪=0.10 significance level?

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Flight times The pilot suspects that the Dubai-to-Doha outbound flight typically takes longer. If so, the difference (Outbound鈭扲eturn) in flight times will be positive on more days than it is negative. What if either flight is equally likely to take longer? Then we can model the outcome on a randomly selected day with a coin toss. Heads means the Dubai-to-Doha outbound flight lasts longer; tails means the Doha-to-Dubai return flight lasts longer. To imitate a random sample of 12days, imagine tossing a fair coin 12times.

a. Find the probability of getting 11or more heads in 12tosses of a fair coin.

b. The outbound flight took longer on 11of the 12days. Based on your result in part (a), what conclusion would you make about the Emirates pilot鈥檚 suspicion?

Music and memory Does listening to music while studying help or hinder students鈥� learning? Two statistics students designed an experiment to find out. They selected a random sample of 30students from their medium-sized high school to participate. Each subject was given 10minutes to memorize two different lists of 20words, once while listening to music and once in silence. The order of the two word lists was determined at random; so was the order of the treatments. The difference (Silence 鈭� Music) in the number of words recalled was recorded for each subject. The mean difference was 1.57and the standard deviation of the differences was 2.70.

a. If the result of this study is statistically significant, can you conclude that the difference in the ability to memorize words was caused by whether students were performing the task in silence or with music playing? Why or why not?

b. Do the data provide convincing evidence at the伪=0.01 significance level that the number of words recalled in silence or when listening to music differs, on average, for students at this school?

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The correlation between the heights of fathers and the heights of their grownup sons, both measured in inches, isr=0.52. If fathers鈥� heights were measured in feet instead, 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.
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