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

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Shariqahmed Shariqahmed · Answer 1 · 2019-12-25T15:59:06+01:00

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 = [tex]P_{0}[/tex] = 0.5

Level of significance = α = 0.02

Step 1:

[tex]H_{0}[/tex]: p = 0.5

[tex]H_{1}[/tex]: p < 0.5 (Left tailed test)

Step 2:

The critical vale is = 2.0537

Step 3:

The test statistic is,

z = [tex]\frac{p - p_{0} }{\sqrt{\frac{p_{0} (1-p_{0}) }{n} } }[/tex]

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.