A sociologist randomly selects 382 females 15 to 19 years old and asks each to disclose her family structure at age 14 and whether she has had sexual intercourse. Use the results in the accompanying table to complete parts (a) through (f) below. Click here to view the data table of family structure and sexual activity. Click here to view the Chi-Square table of critical values, (a) Compute the expected values of each cell under the assumption of independence. Had sexual Both Biological or Adoptive Parent and intercourse Parents Single Parent Stepparent Non-parental Guardian 33 61 64 46 Yes 17 82 No (Round to two decimal places as needed.) (b) Verify that the requirements for performing a chi-square test of independence are satisfied. Select all requirements for a chi-square test of independence. A. All expected frequencies are greater than or equal to 1. B. The expected frequencies are approximately Normal. C. No more than 20% of the expected frequencies are less than 5. D. All expected frequencies are greater than or equal to 5. [)E. All expected frequencies are greater than or equal to 10. (c) Compute the chi-square test statistic. x8 =(Round to three decimal places as needed.) (d) Test whether family structure and sexual activity of 15- to 19-year-old females are independent at the a = 0.05 level of significance. State the hypotheses. Choose the correct answer below. O A. Ho: P1 = P2 = P3 = P4 H, : At least one proportion is different from the others. O B. Ho: Sexual activity and the family structure are independent H, : Sexual activity and the family structure are dependent. O C. Ho: H1 = E, and p4 = E4 and H3 = E3 and #4 = E4 H, : At least one mean is different from what is expected. What range of P-values does the test statistic correspond to? The P-value is Make the proper conclusion. Choose the correct answer below. A. The P-value is less than a, so reject Ho. There is sufficient evidence at the a = 0.05 level of significance to conclude that sexual activity and family structure are related. O B. The P-value is greater than a, so do not reject Ho. There is not sufficient evidence at the a = 0.05 level of significance to conclude that sexual activity and family structure are related. O C. The P-value is greater than a, so reject Ho. There is sufficient evidence at the a = 0.05 level of significance to conclude that sexual activity and family structure are related. O D. The P-value is less than a, so do not reject Ho. There is not sufficient evidence at the a = 0.05 level of significance to conclude that sexual activity and family structure are related. (e) Compare the observed frequencies with the expected frequencies. Which cell contributed most to the test statistic? The cell for females who sexual intercourse and lived with contributed most to the test statistic. Was the expected frequency greater than or less than the observed frequency? The observed frequency was than the expected frequency. What does this information tell you? O A. There were not enough subjects in the sample to form any conclusions from the data. O B. This means that family structure seems to have an effect on whether or not a child has had sexual intercourse. O C. This means that family structure does not seem to have an effect on whether or not a child has had sexual intercourse. (f) Construct a conditional distribution by family structure and draw a bar graph. Does this evidence support your conclusion in part (d)? Fill in the conditional distribution
