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 196 donors, it is found that 29 have hypertension. A scientist claimed that 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 to test the claim.

1) Find the null and the alternative hypothesis.

2) Find the test statistic.

3) Would reject or fail to reject the null hypothesis? Explain.

4) Would you agree or disagree with the scientists claim?

Answer 1

This is a binomial proportion test. The two outcomes are whether the student has hypertension or not.

x = students from sample having hypertension.

x = 29 n = 196

Where = x /n

= 0.148

We want to test whether the percent is higher than 9.2%. So it is right tailed one tailed test.

1) Find the null and the alternative hypothesis.

: p = 9.2% =0.092

: p > 0.092

We can use the normal approximation because 'n > 30' and 'np> 10'

2) Find the test statistic.

Test Stat :

Where the null proportion = 0.092

Test Stat = 2.2065

3) Would reject or fail to reject the null hypothesis? Explain.

Since level of significance is 0.05

Critical value at 5%

=

C.V. = 1.6449   ...............using normal distribution tables

Since |T.S.| > C.V.

We reject the null hypothesis at 5% level. The test Stat falls in the critical region.

4) Would you agree or disagree with the scientists claim?

There is sufficient eivdence to conclude that hypertension in students is higher than 9.2% during the final week. We agreee with the claims.