1. It is believed that nearsightedness affects about 8% of allchildren. In a random sample of 194 children, 21 arenearsighted.
(a) Construct hypotheses appropriate for the following question: dothese data provide evidence that the 8% value is inaccurate?

• Ho: p = .08
  Ha: p ≠ .08
• Ho: p = .08
  Ha: p < .08
• Ho: p = .08
  Ha: p > .08

(b) What proportion of children in this sample arenearsighted?
(round to four decimal places)
(c) Given that the standard error of the sample proportion is0.0195 and the point estimate follows a nearly normal distribution,calculate the test statistic (use the Z-statistic).
Z =  (please round to two decimal places)
(d) What is the p-value for this hypothesis test?
p =  (please round to four decimal places)
(e) What is the conclusion of the hypothesis test?

• Since p ≥ α we do not have enough evidence to reject the nullhypothesis
• Since p<α we reject the null hypothesis and accept thealternative
• Since p<α we fail to reject the null hypothesis
• Since p ≥ α we accept the null hypothesis

2. Test the claim that the mean GPA of night students is largerthan 2.7 at the 0.005 significance level.

(1)The null and alternative hypothesis would be:

a) H0:p≥0.675
H1:p<0.675   

b) H0:p=0.675
H1:p≠0.675

c) H0:μ≤2.7   
H1:μ>2.7

d) H0:p≤0.675   
H1:p>0.675   

e) H0:μ=2.7
H1:μ≠2.7

f) H0:μ≥2.7
H1:μ<2.7

(2) The test is:

-two-tailed

-left-tailed

-right-tailed

(3) Based on a sample of 35 people, the sample mean GPA was 2.73with a standard deviation of 0.04

The p-value is: ____ (to 2 decimals)

Based on this we:

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