Question

This problem is based on information taken from *The Merck
Manual* (a reference manual used in most medical and nursing
schools). Hypertension is defined as a blood pressure reading over
140 mm Hg systolic and/or over 90 mm Hg diastolic. Hypertension, if
not corrected, can cause long-term health problems. In the
college-age population (18-24 years), about 9.2% have hypertension.
Suppose that a blood donor program is taking place in a college
dormitory this week (final exams week). Before each student gives
blood, the nurse takes a blood pressure reading. Of 192 donors, it
is found that 28 have hypertension. Do these data indicate that the
population proportion of students with hypertension during final
exams week is higher than 9.2%? Use a 5% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a
left-tailed, right-tailed, or two-tailed test?

*H*_{0}: *p* = 0.092;
*H*_{1}: *p* < 0.092; left-tailed

*H*_{0}: *p* > 0.092;
*H*_{1}: *p* = 0.092;
right-tailed

*H*_{0}: *p* = 0.092;
*H*_{1}: *p* ≠ 0.092; two-tailed

*H*_{0}: *p* = 0.092;
*H*_{1}: *p* > 0.092; right-tailed

(b) What sampling distribution will you use? Do you think the
sample size is sufficiently large?

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

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.

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) State your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the true proportion of students with hypertension during final exams week is higher than 0.092.

There is insufficient evidence at the 0.05 level to conclude that the true proportion of students with hypertension during final exams week is higher than 0.092

Answer #1

The statistical software output for this problem is :

(a)

Level of significance = 0.01

Option **D** is correct .

(b)

Option **C** is correct.

Test statistics = 2.58

(c)

P-value = 0.0049

(d) Option **A** is correct.

(e) Option **A** is correct.

This problem is based on information taken from The Merck
Manual (a reference manual used in most medical and nursing
schools). Hypertension is defined as a blood pressure reading over
140 mm Hg systolic and/or over 90 mm Hg diastolic. Hypertension, if
not corrected, can cause long-term health problems. In the
college-age population (18-24 years), about 9.2% have hypertension.
Suppose that a blood donor program is taking place in a college
dormitory this week (final exams week). Before each student...

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