Question

1. Women athletes at the University of Jamestown have a long-term graduation rate of 72%. Over the past several years, a random sample of 45 women athletes at the school showed that 30 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 72%?

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

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

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

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

2. A random sample of 300 one-year old baby boys is studied and their weights in pounds are recorded. Their mean weight was 25.7 pounds with a standard deviation 5.3 pounds. A medical researcher claims that the mean weight of one-year old boys is greater than 25 pounds. Does this study provide convincing evidence that the researcher’s claim is true? Use a 0.02 level of significance.

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

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

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

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

Answer 1

1) a) H₀: P = 0.72

H₁: P < 0.72

b) = 30/45 = 0.67

The test statistic z = (- P)/sqrt(P(1 - P)/n)

= (0.67 - 0.72)/sqrt(0.72(1 - 0.72)/45)

= -0.75

P-value = P(Z < -0.75)

= 0.2266

C) At alpha = 0.05, since the p-value is greater than the alpha(0.2266 > 0.05), so we should not reject the null hypothesis.

D) At 5% significance level there is not sufficient evidence to support the claim that the population proportion of women athletes is less than 72%.

2) a) H₀: = 25

H₁: > 25

B) The test statistic z = ()/()

= (25.7 - 25)/(5.3/)

= 8.17

P-value = P(Z > 8.17)

= 1 - P(Z < 8.17)

= 1 - 1 = 0

C) Since the p-value is less than the significance level (0 < 0.02), so we should reject the null hypothesis.

D) So at 0.02 significance level there is sufficient evidence to support the researcher's claim that the mean weight of one-year old boys is greater than 25 pounds.