Question

A student believes that less than 50% of students at his college receive financial aid. A random sample of 120 students was taken. Sixty-five percent of the students in the sample receive financial aid. Test the hypothesis at the 2% level of significance. What are the p-value and conclusion? a. .999; Do not reject H0 b. .02; Reject H0

Answer 1

Answer:

P-value is greater than the significance level, we fail to reject null hypothesis.

Explanation:

Here,  

Sample size = n = 120

Sample proportion = p = 0.6500

Population Proportion = $P_{0}$ = 0.5

Level of significance = α = 0.02

Step 1:

$H_{0}$: p = 0.5

$H_{1}$: p < 0.5 (Left tailed test)

Step 2:

The critical vale is = 2.0537

Step 3:  

The test statistic is,

z =  $\frac{p - p_{0} }{\sqrt{\frac{p_{0} (1-p_{0}) }{n} } }$

Step 5:

Conclusion using critical value: Since the test statistic value is greater than the critical value, we fail to reject null hypothesis.

Step 6:  

Conclusion using P-value: Since the P-value is greater than the significance level, we fail to reject the null hypothesis.