Question

1. A recent study 50 people indicated that 52.4% of people vote. Test the Hypothesis at the a =.05 level that the proportion of people that vote is > 50% 2. A recent study of 25 people indicated that the mean body temperature was 98.2 with a calculated standard deviation of .62. Test the hypothesis at the a = .05 level that the mean body temperature is not equal to 98.6. Since we have a calculated standard deviation, we must use the adjusted normal table (Table-A3). This is an example of a Two Tail Test.

Answer 1

1) given data are sample n = 50

Sample proportion $\widehat{p}$ = 52.4%= 0.524

Population proportion p= 0.50

Null hypothesis H0: - p=0.50

Alternative hypothesis Ha:- p>0.50

Level of significance $\alpha$ =0.05

Test statistic: - z= $(\widehat{p}-p)/\sqrt{p (1-p)/n}$

Z=(0.524-0.50)/$\sqrt{0.5(0.5)/50}$

= 0.024/ 0.0707

= 0.3394

Critical region: - at 5% level in right tail from z table z = 1.645 ( it is a one tail test because p>0.50)

Reject the null hypothesis H0 if zcal> 1.645

Decision:- fail to reject the null hypothesis H0 because the zcal is less than z critical value

I.e, 0.3394 < 1.645

Conclusion: - their is no sufficient evidence to support the claim, that" proportion of people that vote is >50%"