Question

1. It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) Construct hypotheses appropriate for the following question: do these 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 are nearsighted?
(round to four decimal places)
(c) Given that the standard error of the sample proportion is 0.0195 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 null hypothesis
• Since p<α we reject the null hypothesis and accept the alternative
• 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 larger than 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 2.73 with 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

Answer 1