Question

25.35 Comparing two proportions and the chi-square test. The popularity of computer, video, online, and virtual reality games has raised concerns about their ability to negatively affect youth, although the existing literature has been inconsistent. A recent survey of 14- to 18-year-olds in Connecticut high schools compared, among other things, aggressive behavior as evidenced by getting into serious fights for girls who have and have not played video games. When comparing two proportions such as these, the data can be presented in a two-way table containing the counts of successes and failures in both samples, with two rows and two columns. Here are the data presented in this manner: 17 Serious Fights Yes No Played games Never played games 36 578 1436 (a) Is there evidence that the proportions of all 14- to 18-year-old girls who played or have never played video games and have gotten into serious fights differ? Find the two sample proportions, the z statistic, and its P-value (b) Is there evidence that the proportions for 14- to 18-year-old girls who have or have not gotten into serious fights differ between those who have played or have never played video games? Find the chi-square statistic and its P-value (c) show that (up to roundoff error) your is the sarne as z·The two P-values are also the same. These facts are always true, so you will often see chi-square for 2 x 2 tables used to compare two (d) Suppose we were interested in finding out if the data gave good evidence that video gaming was associated with increased aggression in girls as evidenced by getting into serious fights. Can we use the z test for this hypothesis? What about the x test? What is the important difference between these two procedures?

Answer 1

Excel add-in (Mega Stat) procedure: Step 1: In EXCEL, Select Add-Ins> Mega Stat > Hypothesis Tests. Step 2: Choose Proportion vs. Hypothesized Value. Step 3: Choose Data Input Step 4: In Group l, enter the value 36 underx and enter the value 91 under n Step 5: In Group 2, enter the value 578 under x and enter the value 2014 under n. Step 6: Enter 0 Under Hypothesized difference. Step 7: Choose not equal in alternative. Step 8: Click OK. Excel add-in (Mega Stat) output:

Hypothesis test for two independent proportions 0.2917 p (as decimal) 36/91 578/2014 614/2105 p (as fraction) 0.3956 0.287 36 91 578 2014 614. X 2105 n 0.1086 difference 0. hypothesized difference 0.0487 std. error 2.23 z 0258 p-value (two-tailed) The two sample proportions are 0.3956, 0287 The value of test statistic is z 2.23 and the p-value is 0.0258 Since p-value (-0.0258) < α (-0.05). then reject the null hypothesis Therefore, the proportion of 14-to 18 year-old girls who played or have never played video games and have gotten into serious fight differs