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== From the given information, sample size n = -313, X = 53,P=16% = 0.16, and a= 0.05. X 53 Sample proportion 0.1693 313 For this study, we should use Z-test for proportion. Null hypothesis Ho: P=0.16, Alternative hypothesis H,:P+0.16, The test is two-tailed test Level of significance be a = 0.05, then the critical values are $ 20.05/2 = +1.96. Critical regions: Z <-1.96 and 2 > 1.96.
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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 0.1693-0.16 The test statistic value is Zcal = 0.4488 P(1-P) (0.16x(1 – 0.84)) 313 The value of the test statistic ZcQ = 0.4488 lies between the critical values, it falls in the acceptance region. We fail to reject the null hypothesis. P-value=2P(Z > 0.45) = 2(0.3264) = 0.6528.
P-value 0.6528 greater than the level of significance a= 0.05, we fail to reject the null hypothesis. The data suggest the population proportion is not significantly different from 16% at a = 0.05, so there is sufficient evidence to conclude that the percentage of financial aid recipients who volunteer is equal to 16%. =
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