A group of retired admirals, generals, and other senior military leaders, recent

Question

A group of retired admirals, generals, and other senior military leaders, recently published a report, "Too Fat to Fight".

The report said that 75 percent of young Americans between the ages of 17 to 24 do not qualify for the military because of

failure to graduate [from high school],

criminal records or

physical problems.

The study cited Department of Defense and health data. A research group does not agree with this statistic.

In a random sample of 180 young Americans 125 did not qualify for the military.

Using a 5% significance level, is there sufficient evidence to conclude that less than 75% of Americans between the ages of 17 to 24 do not qualify for the military?

Question 15

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What are the null and alternative hypotheses?

Select one:

a. H0: p < 0.75 and HA: p = 0.75

b. H0: p = 0.75 and HA: p > 0.75

c. H0: p = 0.75 and HA: p < 0.75

d. H0: p = 0.694 and HA: p < 0.694

Question 16

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What is the test statistic?

Select one:

a. z = 0.75

b. z = 0

c. z = 0.694

d. z = -1.72

Question 17

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What is the p-value?

Select one:

a. p-value = 0.9574

b. p-value = -1.72

c. p-value = 0.0426

d. p-value = 0.0852

Question 18

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What is the appropriate conclusion?

Select one:

a. Reject H0. There is not enough evidence to say that less than 75% of Americans between the ages of 17 to 24 do not qualify for the military.

b. Do not reject H0. There is not enough evidence to say that less than 75% of Americans between the ages of 17 to 24 do not qualify for the military.

c. Accept H0. There is enough evidence to say that less than 75% of Americans between the ages of 17 to 24 do not qualify for the military.

d. Reject H0. There is enough evidence to say that less than 75% of Americans between the ages of 17 to 24 do not qualify for the military.

Explanation / Answer

The statistical softwre output for this problem is:

One sample proportion hypothesis test:
p : Proportion of successes
H0 : p = 0.75
HA : p < 0.75

Hypothesis test results:

Hence,

Answer - 15: H0: p = 0.75 and HA: p < 0.75

Option C is correct.

Answer - 16: z = -1.72

Option D is correct.

Answer - 17: p-value = 0.0426

Option C is correct.

Answer - 18: Reject H0. There is enough evidence to say that less than 75% of Americans between the ages of 17 to 24 do not qualify for the military.

Option D is correct.

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 125 180 0.69444444 0.032274861 -1.7213259 0.0426

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