The University of Chicago’s General Social Survey (GSS) is the nation’s most imp

ID: 3155562 • Letter: T

Question

The University of Chicago’s General Social Survey (GSS) is the nation’s most important social science sample survey. The GSS regularly asks its subjects their astrological sign. Since the 12 zodiac signs evenly divide the calendar year, this information can be used to test whether births are uniformly distributed across the year. Here is an incomplete Minitab output for the corresponding chi-square test:

Test Contribution

Category Observed Proportion Expected to Chi-Sq

Aquarius 224 0.0833333 231.583 0.248

Aries 225 0.0833333 231.583 0.187

Cancer 240 0.0833333 231.583 0.306

Capricorn 216 0.0833333 231.583 1.047

Gemini 241 0.0833333 231.583 0.383

Leo 260 0.0833333 231.583 3.487

Libra 243 0.0833333 231.583 0.563

Pisces 244 0.0833333 231.583 0.666

Sagittarius 200 0.0833333 231.583 4.307

Scorpio 214 0.0833333 231.583 1.335

Taurus 222 0.0833333 231.583 0.397

Virgo 250 0.0833333 231.583 1.465

N DF Chi-Sq P-Value

2779 * * *

13. The P-value of this test is

a. greater than 0.10.

b. below 0.10 but above 0.05.

c. below 0.05 but above 0.01.

d. below 0.01.

14. The chi-square test in this situation

a. is valid, because the sample is random and the expected counts are large enough.

b. is valid, because the sample is random and the observed counts are large enough.

c. is valid, because the sample size is large.

d. is not valid, because we do not know the true population proportions.

15. At significance level alpha 5%, you conclude

a. that there is significant evidence that births are not uniformly distributed across the year.

b. that the data are consistent with a uniform distribution of births across the year.

c. that the data prove that births are uniformly distributed across the year.

d. nothing, because the test assumptions are not met.

Explanation / Answer

0.248

0.187

0.306

1.047

0.383

3.487

0.563

0.666

4.307

1.335

0.397

1.465

Total

14.391