Question

1 2 3 4 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 scientist’s claim?

Answer 1

Solution :

1) The null and alternative hypotheses are as follows :

H​​​​​​0 : p = 9.2% = 0.092 i.e. The population proportion of students with hypertension during final exams week is 9.2%.

H​​​​​​1 : p > 9.2% i.e. The population proportion of students with hypertension during final exams week is higher than 9.2%.

2) We shall use z-test to test the hypothesis. The test statistic is given as follows :

Where, p̂ is sample proportion, p is hypothesized value of population proportion under H​​​​​​0, n is sample size.

Sample proportion of students who had hypertension is,



p = 0.091

n = 196

The value of the test statistic is 2.7106.

3) Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test, which is given as follows :

p-value = P(Z > value of the test statistic)

p-value = P(Z > 2.7106)

p-value = 0.0034

The p-value is 0.0034.

Significance level = 5% = 0.05

(0.0034 < 0.05)

Since, p-value is less than the significance level of 5%, therefore we shall reject the null hypothesis (H​​​​​​0) at 5% significance level.

4) At 5% significance level, there is sufficient evidence to support the scientist claim that the population proportion of students with hypertension during final exams week is higher than 9.2%.