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A university claims that their employment rate directly after graduation is 40%. In a sample of 100 graduates, 32 found to have gained employment directly after graduation. Test the claim that the university's employment rate after graduation is smaller than 40% at the 0.10 significance level.

The null and alternative hypothesis would be:

H0:p≥0.4 0:≥0.4

H1:p<0.4 1:<0.4

H0:μ=0.4 0: =0.4

H1:μ≠0.4 1: ≠0.4

H0:μ≤0.4 0: ≤0.4

H1:μ>0.4 1: >0.4

H0:p≤0.4 0: ≤0.4

H1:p>0.4 1: >0.4

H0:p=0.4 0: =0.4

H1:p≠0.4 1: ≠0.4

H0:μ≥0.4 0: ≥0.4

H1:μ<0.4 1: <0.4

The test is:

right-tailed

two-tailed

left-tailed

The test statistic is: (to 2 decimals)

The p-value is: (to 4 decimals)

Based on this we:

Reject the null hypothesis

Fail to reject the null hypothesis

Given:

n = 100

x = 32

Population Proportion, p = 0.40

Significance level, = 0.10

Solution:

Sample proportion: