Since the Pvalue is 0005 which is less than the significance

Since the P-value is 0.005 which is less than the significance level of 0.01, the decision is to reject the null hypothesis. There is strong evidence to say that more than 75% of adults agree that it is morally wrong to not report all income on tax returns.

1. Women athletes at the University of Jamestown have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%?

a. State the null (H0) and alternative (H1) hypotheses.

b. Give the test statistics and the p-value for this significance test.

c. Make a decision on whether or not to reject the null hypothesis.

d. Summarize the conclusion in the context of this problem.

Solution

(a)

H0: p = 0.67
H1: p < 0.67

(b)
np = 38 * 0.67 = 25.46 > 5 is true
np = 38 * 0.33 = 12.54 > 5 is true
phat = 21 / 38 = 0.55
z = (0.55 - 0.67)/SQRT{0.67 * 0.33 / 38}
= -0.12 / 0.08
= -1.5

P(z < 0.55) = 1 - P(z > -1.5) = 1 - 0.9332
P-value = 0.0668

(c)
P-value <= alpha is false. We do not reject H0

(d)

At a 5% level of significance, sample data indicates that the proportion of women athletes who graduate from the University of Jamestown is not less than 0.67%.