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 20 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance.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.)

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Asked Nov 8, 2019
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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 20 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance.

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.)

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Expert Answer

Step 1

It is given that women athletes have a long term graduation rate is 67% and the level of significance is 0.01

 

That is, P 0.67 and a 0.01
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That is, P 0.67 and a 0.01

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Step 2

The sample proportion is calculated below:

Thus, the sample proportion is 0.55.

 

p
n
20
36
=0.55
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p n 20 36 =0.55

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Step 3

The value of the sample test statistic is given below:

Therefore, the va...

р-Р
Z=
P(1-Р)
п
0.55-0.67
0.67(1-0.67)
36
-0.12
0.2211
36
-0.12
V0.006142
-0.12
0.078
=-1.53
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р-Р Z= P(1-Р) п 0.55-0.67 0.67(1-0.67) 36 -0.12 0.2211 36 -0.12 V0.006142 -0.12 0.078 =-1.53

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