Question

A university claims that their employment rate directly after graduation is 10%. In a sample of 100 graduates, 5 found to have gained employment directly after graduation. Test the claim that the university's employment rate after graduation is smaller than 10% at the 0.025 significance level.

The null and alternative hypothesis would be:

H0:μ≥0.1H0:μ≥0.1
H1:μ<0.1H1:μ<0.1

H0:p=0.1H0:p=0.1
H1:p≠0.1H1:p≠0.1

H0:μ=0.1H0:μ=0.1
H1:μ≠0.1H1:μ≠0.1

H0:μ≤0.1H0:μ≤0.1
H1:μ>0.1H1:μ>0.1

H0:p≥0.1H0:p≥0.1
H1:p<0.1H1:p<0.1

H0:p≤0.1H0:p≤0.1
H1:p>0.1H1:p>0.1

The test is:

two-tailed

left-tailed

right-tailed

The test statistic is:  (to 2 decimals)

The p-value is:  (to 4 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0:p≥0.10

Ha : p < 0.10

= x / n = 5/100=0.05

P0 = 0.10

1 - P0 =1-0.10=0.9

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.05 - 0.10 / [(0.10*0.9) / 100]

z=-1.67

P(z < -1.67) = 0.0475

P-value = 0.0475

= 0.025

P-value >

fal to Reject the null hypothesis .