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A sociologist randomly selects 376 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. 33 Had sexual intercourse Both Biological or Adoptive Parents Single Parent Parent and Non-parental Guardian Stepparent 58 62 43 Yes 18 (Round to two decimal places as needed.) (b) Verify that the requirements for performing a chi-square test of independence are satised. Select all requirements for a chi-square test of independence. I: A. No more than 20% of the expected frequencies are less than 5. I: B. All expected frequencies are greater than or equal to 5. 0 Data table 0f family structure and sexual actIVIty I: C. The expected frequencies are approximately Normal. I: D' A\" exDSCted frequemies are greater than or equal to 10' Had sexual Both Biological Single Parent Parent and Non-parental |: E. All expected frequencies are greater than or equal to 1. intercourse 0f AdOPtiVe Stepparent Guardian Parents (1:) Compute the chi-square test statistic. 58 43 33 37 18 X3 = |: (Round to three decimal places as needed.) Click to select your answer(s). (d) Test whether family structure and sexual activity of 15- to 19-year-old females are independent at the a = 0.1 level of significance. State the hypotheses. Choose the correct answer below. O A. Ho: Sexual activity and the family structure are independent. H: Sexual activity and the family structure are dependent. O B. Ho: P1 = P2 = P3 = P4 H : At least one proportion is different from the others. O C. Ho: H1 = E, and H4 = E4 and H3 = E3 and H4 = E4 Hy: 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 prope t answer below. between .01 and .025. O A. The P-v between .025 and .05. 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 B. The P-v less than .01. There is sufficient evidence at the a = 0.05 level of significance to conclude that sexual activity and family structure are related. O C. The P-v between .05 and . 10. ect Ho. There is not sufficient evidence at the a = 0.05 level of significance to conclude that sexual activity and family structure are related. greater than . 10.Make the proper conclusion. Choose the correct answer below. O A. 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 B. The P-value is less than a, so reject Ho. There is sufficient evidence at the o = 0.05 level of significance to conclude that sexual activity and family structure are related. C. 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. O D. 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. (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 freque both parents The observed frequency was than the expected frequency. a non-parental guardian What does this information tell you? a parent and a stepparent O A. This means that family structure does not seem to have an effect o a single parent xual intercourse.What does this information tell you? O A. This means that family structure does not seem to have an effect on whether or not a child has had sexual intercourse. O B. This means that family structure seems to have an effect on whether or not a child has had sexual intercourse. O C. There were not enough subjects in the sample to form any conclusions from the data. (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. (Round to three decimal places as needed.) Had sexual Intercourse Both Biological or Adoptive Parents Single Parent Parent and Non-parental Guardian Stepparent Yes No Let 1 = Both, 2 = Single, 3 = Stepparent, and 4 = Guardian. Choose the correct bar graph below. 0 A. O B. 3-: Ives 3-5: 0.2 IND 0.2 0 1 2 3 4 1 2 3 O C. O D. 3-: .Y. 3-: 0.2 IND 0.2 0 1 2 3 4 0 1 2 3 Does this evidence support the previous conclusion? O A. Yes, because the bars are the same height in each family structure, but different across family structures. O B. No, because the height of the "did not have sexual intercourse" bar is the same across all the family structures. O C. No, because the height of the "had sexual intercourse" bar is the same across all the family structures. O D. Yes, because there are obvious changes in the heights of each pair of bars across the family structures. I Yes I Yes
