Homework SourseQuestion 1 Determine if the problem is either a test of hypo
Question
1. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the
Solution
1)This is a hypothesis testing problem
| We have n = 500, sample proportion p = 415 / 500 = 0.83 and P = 0.85 we want to test whether hypothesis: H0: true P >= 0.85 (null hypothesis) H1: true P < 0.85 (alternative hypothesis) This is lower tail test (because P < 0.85 suggests Z < test statistic showing left tailed area) now, calculating statistics, (test statistic) sigma s = sqrt(P*(1-P)/n) = 0.016 z-score = (p-P)/s = -1.25 this is lower tailed test, hence p-value = P( z < -1.25) = 0.1056 since p-value = 0.1056 is more than significance level (0.05), we fail to reject null hypothesis, there is not enough evidence to conclude that the true population proportion of households having the family room as the primary television location is actually less than .85 |
