Question

Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 36 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 10% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: p = 0.67; H1: p ≠ 0.67

H0: p = 0.67; H1: p < 0.67   

H0: p < 0.67; H1: p = 0.67

H0: p = 0.67; H1: p > 0.67

(b) What sampling distribution will you use?

The Student's t, since np > 5 and nq > 5.

The Student's t, since np < 5 and nq < 5.   

The standard normal, since np > 5 and nq > 5.

The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.   

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.10 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

There is insufficient evidence at the 0.10 level to conclude that the true proportion of women athletes who graduate is less than 0.67.    

Weatherwise magazine is published in association with the American Meteorological Society. Volume 46, Number 6 has a rating system to classify Nor'easter storms that frequently hit New England states and can cause much damage near the ocean coast. A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating.

(a) Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. What would be the null hypothesis regarding average wave height?

μ = 16.4

μ > 16.4   

μ < 16.4

μ ≠ 16.4

(b) If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis?

μ ≠ 16.4

μ = 16.4   

μ < 16.4

μ > 16.4

(c) If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis?

μ = 16.4

μ ≠ 16.4   

μ < 16.4

μ > 16.4

(d) Suppose you do not know if the storm is getting worse or dying out. You just want to test the hypothesis that the average wave height is different (either higher or lower) from the severe storm class rating. What would you use for the alternate hypothesis?

μ = 16.4

μ ≠ 16.4   

μ < 16.4

μ > 16.4

(e) For each of the tests in parts (b), (c), and (d), would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?

both; left; right

left; both; right   

right; left; both

left; right; both

Answer 1