Question

A decade-old study found that the proportion, p, of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 220 high school seniors in his random sample, 179 believe that getting rich" is an important goal. Can he conclude, at the 0.05 level of significance, that the proportion has indeed changed? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. 0 р The null hypothesis: X $ A The alternative hypothesis: (Choose one) OSO 00 The type of test statistic DWD D< > The value of the test statistike: (Round to at least three decimal places.) 0 x 6 ? The two critical values at the 0.05 level of cance: Round to at least three decimal places.) and D Can we condute that the proportion of high school seriors who believe that getting rich" is an important goal has changed? Yes No

Answer 1

== From the given information, sample size n = 220,X = 179, P = 80% = 0.80, and a=0.05. X 179 Sample proportion -= 0.8136 220 For this study, we should use Z-test for proportion. Null hypothesis H. : P=0.80, Alternative hypothesis 4,:P+0.80, Level of significance be a = 0.05, then the critical values are $2005a = £1.96. Critical regions: Z <-1.96 and 2 > 1.96. If the test statistic value falls between - 1.96 and 1.96, we fail to reject the null hypothesis. Otherwise, we reject the null hypothesis. P-P 0.8136 -0.80 The test statistic value is Za = 0.5043 P(1-P) (0.80×(1-0.80)) 220 The value of the test statistic Zca = 0.5043 lies between the critical values, it falls in the acceptance region. We fail to reject the null hypothesis. P-value=2P(Z >0.50) = 2(0.3085) = 0.6170. P-value 0.6170 greater than the level of significance a = 0.05, we fail to reject the null hypothesis. There is no enough evidence to conclude that at the 5% level of significance, that the proportion has indeed changed.