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 38 women athletes at the school showed that 22 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?

0.05

State the null and alternate hypotheses.

*H*_{0}: *p* < 0.67;
*H*_{1}: *p* = 0.67

*H*_{0}: *p* = 0.67;
*H*_{1}: *p* ≠ 0.67

*H*_{0}: *p* = 0.67;
*H*_{1}: *p* < 0.67

*H*_{0}: *p* = 0.67;
*H*_{1}: *p* > 0.67

(b) What sampling distribution will you use?

The Student's *t*, since *np* > 5 and
*nq* > 5.

The standard normal, since *np* > 5 and *nq*
> 5.

The standard normal, since *np* < 5 and *nq*
< 5.

The Student's *t*, since *np* < 5 and
*nq* < 5.

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.)

Sketch the sampling distribution and show the area corresponding
to the *P*-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 α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 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 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

There is insufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

Answer #1

*Null and
Alternative Hypotheses*

The following null and alternative hypotheses need to be tested:

*Sampling
distribution*

The standard normal, since *np* > 5 and *nq*
> 5.

(b)

*Test
Statistics*

The z-statistic is computed as follows:

(c)

The p-value is p = 0.1163

*Graphically*

(d)

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

There is insufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

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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 39 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?
State the null and alternate hypotheses.
H0: p = 0.67;
H1: p ≠...

Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 39 women athletes at the school showed that 22 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? State the null and
alternate hypotheses. H0: p = 0.67; H1: p <...

Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 38 women athletes at the school showed that 19 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.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p = 0.67; H1: p ≠...

Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 37 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?
State the null and alternate hypotheses.
H0: p = 0.67;
H1: p ≠...

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 1% level of significance. (a) What is the level of
significance? State the null and alternate hypotheses. H0: p =
0.67; H1: p >...

Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 38 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 1% level of significance. (a) What is the level of
significance? State the null and alternate hypotheses. H0: p =
0.67; H1: p >...

Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 38 women athletes at the school showed that 22 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?
State the null and alternate hypotheses.
H0: p = 0.67;
H1: p ≠
0.67H0:...

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.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p < 0.67;
H1: p =
0.67H0:...

Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 41 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 1% level of significance. (a) What is the level of
significance? 0.01 Correct: Your answer is correct. State the null
and alternate hypotheses. H0:...

Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 39 women athletes at the school showed that 22 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?
State the null and alternate hypotheses.
H0: p = 0.67;
H1: p <...

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