Question

Women athletes at 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%

Answer 1

No this does not indicate that the population proportion of women athletes who graduate from the university is now less than 67%.

Given long term graduation rate of 67%, sample size of 36  and the women athletes graduated is 23.

We have to find whether  the given information shows  that the population proportion is less than 67%.

First we have to create hypothesis for this :

$H_{0}$:P=0.67

$H_{1}$:P<0.67

Under null hypothesis the test statistic is

z=p bar-p/$\sqrt{p(1-p)/n}$

where p bar=23/36

=0.638

z=(0.638-0.67)/$\sqrt{0.67(1-0.67)/36$

=-0.032/$\sqrt{0.67*0.33/36}$

=-0.032/$\sqrt{0.0064}$

=-0.032/0.078

=-0.41

Now we have to find the left tailed critical at 0.01 significance level using z table.

z=-2.33

Since the z value does not fall in the critical region,therefore we fail to reject the null hypothesis. So we can conclude that there is not sufficient evidence to say that the population proportion of women athletes who graduate from the university is now less than 67%.

Learn more about z test at https://brainly.com/question/14453510

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Question is incomplete as it should specify the signficance level of 0.01 to be used.