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Chapter 11: Q 10. (page 718)

What鈥檚 your sign? The University of Chicago鈥檚 General Social Survey (GSS) is the nation鈥檚 most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random sample of people their astrological sign. Here are the counts of responses from a recent GSS of 4344 people:

If births are spread uniformly across the year, we expect all 12 signs to be equally likely. Do these data provide convincing evidence at the 1% significance level that all 12 signs are not equally likely?

Short Answer

Expert verified

There isn't enough information to back up the assertion that all 12 signals aren't equally likely.

Step by step solution

01

Given information

02

Calculation

The null and alternative hypotheses:

H0:p1=p2=...=p12=112=0.0833Ha:Atleastoneofthepi鈥�sisincorrect.

Using excel:

Chi-square test statistic =19.76

The p-value =0.0487

Decision: Thep-value>0.01fail to reject H0

There isn't enough information to back up the assertion that all 12 signals aren't equally likely.

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Most popular questions from this chapter

Popular kids Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed in Michigan to examine the factors that determine social status for children in grades 4,5,and 6. Researchers administered a questionnaire to a random sample of 478students in these grades. One of the questions asked, "What would you most like to do at school: make good grades, be good at sports, or be popular?" The two-way table summarizes the students' responses. Is there convincing evidence of an association between gender and goal for students in grades 4,5,and 6?

The nonprofit group Public Agenda conducted telephone

interviews with three randomly selected groups of parents of high school children. There

were 202 black parents, 202 Hispanic parents, and 201 white parents. One question asked,

鈥淎re the high schools in your state doing an excellent, good, fair, or poor job, or don鈥檛 you

know enough to say?鈥� Here are the survey results:

Do these data provide convincing evidence that the distributions of opinion about high

schools differ for the three populations of parents?

鈥淲ill changing the rating scale on a survey affect how people answer the question?鈥� To find out, the group took an SRS of 50students from an alphabetical roster of the school鈥檚 just over 1000students. The first 22students chosen were asked to rate the cafeteria food on a scale of 1(terrible) to 5(excellent). The remaining 28students were asked to rate the cafeteria food on a scale of 0(terrible) to 4(excellent). Here are the data:

The students decided to compare the average ratings of the cafeteria food on the two scales.

a. Find the mean and standard deviation of the ratings for the students who were given the 1to5scale.

b. For the students who were given the 0to4scale, the ratings have a mean of 3.21and a standard deviation of 0.568. Since the scales differ by one point, the group decided to add 1to each of these ratings. What are the mean and standard deviation of the adjusted ratings?

c. Would it be appropriate to compare the means from parts (a) and (b) using a two-sample t test? Justify your answer

Aw, nuts! Refer to Exercise 1.

a. Confirm that the expected counts are large enough to use a chi-square distribution to calculate the P-value. What degrees of freedom should you use?

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

c. What conclusion would you draw about the company鈥檚 claimed distribution for its deluxe mixed nuts?

No chi-square The principal in Exercise 7 also asked the random sample of students to record whether they did all of the homework that was assigned on each of the five school days that week. Here are the data:
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