Question

The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her listeners are at least 22 years old and wants to know what age group she should gear her advertisements to for the games. She takes a random sample of 45 listeners from age 22-39 and 55 listeners who are 40 and older and asks them if they are likely to tune in to football games. The "yes" responses are recorded below. Age 22-39 (Group 1) / Age 40+ (Group 2) Responded “Yes” to Football 32 44 Sample Sizen 45 55 At the 0.05 level of significance, is there a significant difference in the proportion of listeners based on age? Enter the test statistic - round to 4 decimal places. Enter the P-Value - round to 4 decimal places. Is there evidence to suggest that there is a significant difference in the proportion of listeners based on age?

Answer 1

Date: 21/11/2019 Answer To test the hypothesis is that there is a significant difference in the proportion of listeners based on age at 5% significance level The null and alternative hypothesis is, Ho: P1 P2 Ha:P1 P2 The z-test statistics is, By using Excel software, find z-test statistics with the help of following steps: 1) 2) 3) 4) 5) 6) Import the data. Select the MegaStat from Add-Ins option. Select the Compare Independent Two Proportions from Hypothesis Tests Select data input. Select Confidence level, Test difference and alternative hypothesis Click Ok.

Hypothesis test for two independent proportions p 1 p2 Pc 0.76 p (as decimal) 76/100 p (as fraction) 0.8 0.7111 32/45 44/55 32 44 76. X 45 55 100 n -0.0889 difference 0. hypothesized difference 0.0858 std. error -1.0354 z 3005 p-value (two-tailed) From the Excel output, the z-test statistics is -1.0354 The p-value for this test is, From the Excel output, the p-value for this test is 0.3005

Decision The conclusion is that the p-value in this context is higher than 0.05 which is 0.3005, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that there is a significant difference in the proportion of listeners based on age. The result is not statistically significant