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 40 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 5% level of significance.

(a) What is the level of significance?

(b) State the null and alternate hypotheses.

(c) What sampling distribution will you use?

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

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

Answer 1

a)

Level of significance = 0.05

b)

H0: p = 0.67

Ha: p < 0.67

c )

Sampling distribution of proportion is approximately normal (z )

d)

Sample proportion = 23 / 40 = 0.575

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= ( 0.575 - 0.67) / sqrt [ 0.67 ( 1 - 0.67) / 40 ]

= -1.28

e)

p-value = P(Z < z)

= P(Z < -1.28 )

= 0.1003 (From Z table)

Since p-value > 0.05 level, fail to reject H0.