Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of40women athletes at the school showed that21eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a1%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:p0.67

H₀:p< 0.67;H₁:p= 0.67

(b) What sampling distribution will you use?

The standard normal, sincenp> 5 andnq> 5.

The Student'st, sincenp> 5 andnq> 5.

The Student'st, sincenp< 5 andnq< 5.

The standard normal, sincenp< 5 andnq< 5.

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

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

Sketch the sampling distribution and show the area corresponding to theP-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?

At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant

At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the= 0.01 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 0.01 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

There is insufficient evidence at the 0.01 level to conclude that the true proportion of women athletes who graduate is less than 0.67.