Question

The New York Times reported a study conducted by the Henry J. Kaiser Family Foundation concerning the role of media in the lives of children (Dylan Loeb McClain. “Where Is Today’s Child? Probably Watching TV,” The New York Times, December6, 1999, C1.). In one question of the study, children were asked if they use a computer each day . From a sample of asked 1,090 children between the age of 2 and 7,283 used a computer each day. From a sample of 2,065 children between the ages of 8 and 18, 1053 used a computer each day.

a. At the 0.05 level o f significance, is there evidence of a significant difference , between the two age groups in the proportion of children that use a computer each day?

Answer 1

Decision:as test statistic is in rejection region we reject null hypothesis

null Hypothesis alternate Hypothesis: Ho: Pi-P2 Pi-P2 0.0000 Ha: 0.0000 for 0.05 level with two tailed test , critical value of Decision rule 1.960 reject Ho if absolute value of test statistic z >1.96 age 2-7 283 0.2596 1090 age 8-18 1053 0.5099 2065 0.2503 0.4235 estimated difference in proportion estimator of pooled proportion p(xtX2/(n+n2) std error Se- 0.0185 test statz- (pi-p2)/Se -13.53

Conclusion: we have sufficient evidence to conclude that there is significant difference between the two age groups in the proportion of children that use a computer each day