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Chapter 11: Q 24. (page 718)

Do students who read more books for pleasure tend to earn higher grades in English? The boxplots show data from a simple random sample of 79 students at a large high school. Students were classified as light readers if they read fewer than 3 books for pleasure per year. Otherwise, they were classified as heavy readers. Each student鈥檚 average English grade for the previous two

marking periods was converted to a GPA scale, where A=4.0,A鈭�=3.7,B+=3.3

and so on.

Short Answer

Expert verified

The distributions of both types seem to be approximately symmetric.

Step by step solution

01

Given information

02

Calculation

Because the median for the Light data set sits more to the left, the box plot of Light readers seems to have a lower center than that of Heavy readers.

Because the distance between the whiskers of the boxplot is bigger for the Light data set, the spread of Light readers is greater than that of Heavy readers. Both sorts of distributions appear to be roughly symmetric.

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Most popular questions from this chapter

Which of the following statements about chi-square distributions are true?

I. For all chi-square distributions, P(x2鈮�0)=1

II. A chi-square distribution with fewer than 10degrees of freedom is roughly symmetric.

III. The more degrees of freedom a chi-square distribution has, the larger the mean of the distribution.

a. I only

b. II only

c. III only

d. I and III

e. I, II, and III

Is your random number generator working? Use your calculator鈥檚 RandInt function to generate 200 digits from 0 to 9 and store them in a list.

a. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator鈥檚 random number generator gives each digit an equal chance of being generated.

b. Carry out a test at the 伪=0.05 significance level. Hint: To obtain the observed

counts, make a histogram of the list containing the 200 random digits, and use the trace feature to see how many of each digit were generated. You may have to adjust your window to go from 鈭�0.5to9.5 with an increment of 1

c. Assuming that a student鈥檚 calculator is working properly, what is the probability that the student will make a Type I error in part (b)?

d. Suppose that 25 students in an AP庐 Statistics class independently do this exercise for homework and that all of their calculators are working properly. Find the probability that at least one of them makes a Type I error.

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of 100students and asks them, 鈥淲hich type of food do you prefer: Ramen, tacos, pizza, or hamburgers?鈥� Here are her data:

The chi-square test statistic is

a. (18鈭�25)225+(22鈭�25)225+(39鈭�25)225+(21鈭�25)225

b. (25鈭�18)218+(25鈭�22)222+(25鈭�39)239+(25鈭�21)221

c. (18鈭�25)25+(22鈭�25)25+(39鈭�25)25+(21鈭�25)25

d. (18鈭�25)2100+(22鈭�25)2100+(39鈭�25)2100+(21鈭�25)2100

e. (0.18鈭�0.25)20.25+(0.22鈭�0.25)20.25+(0.39鈭�0.25)20.25+(0.21鈭�0.25)20.25

Last python Refer to Exercises 28 and 30.

a. Verify that the conditions for inference are met.

b. Use Table C to find the P-value. Then use your calculator鈥檚 蠂2 cdf command.

c. Interpret the P-value from the calculator.

d. What conclusion would you draw using 伪=0.10?

A study conducted in Charlotte, North Carolina, tested the effectiveness of three police responses to spouse abuse: (1)advise and possibly separate the couple, (2)issue a citation to the offender, and (3)arrest the offender. Police officers were trained to recognize eligible cases. When presented with an eligible case, a police officer called the dispatcher, who would randomly assign one of the three available treatments to be administered. There were a total of 650cases in the study. Each case was classified according to whether the abuser was arrested within 6months of the original incident.

a. Explain the purpose of the random assignment in the design of this study.

b. State an appropriate pair of hypotheses for performing a chi-square test in this setting.

c. Assume that all the conditions for performing the test in part (b) are met. The test yields x2=5.063x2=5.063and aP-valueof0.0796. Interpret this P-value.

d. What conclusion should we draw from the study?
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