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 39 women athletes at the school showed that 22 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 5% level of significance.
(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: p = 0.67; H₁: p < 0.67H₀: p = 0.67; H₁: p > 0.67    H₀: p < 0.67; H₁: p = 0.67H₀: p = 0.67; H₁: p ≠ 0.67

(b) What sampling distribution will you use?

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

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?

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

Answer 1