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 21 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?

(b) State the null and alternate hypotheses.

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

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

Answer 1

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 21 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?

level of significance = 0.10

(b) State the null and alternate hypotheses.

Ho: P=0.67, H₁: P < 0.67

Lower tail test

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

Z= -1.11

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

P=0.1344

Since calculated P=0.1344 > 0.10 level of significance, Ho is not rejected.

There is no evidence to indicate that the population proportion of women athletes who graduate from the university is now less than 67%.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.67
Level of Significance	0.1
Number of Items of Interest	21
Sample Size	36
Intermediate Calculations
Sample Proportion	0.583333333
Standard Error	0.0784
Z Test Statistic	-1.1059
Lower-Tail Test
Lower Critical Value	-1.2816
p-Value	0.1344
Do not reject the null hypothesis