This problem is based on information taken from The Merck Manual (a reference ma

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 190 donors, it is found that 27 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% eve ofsignificance. (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? O Ho: p-0.092; HI : p # 0.092; two-tailed Ho: p = 0.092; HI : p 0.092; right-tailed O Ho: p > 0.092; HI, p = 0.092; right-tailed (b) What sampling distribution will you use? Do you think the sample size is sufficiently large? The standard normal, since np > 5 and nq > 5. O The Student's t, since np> 5 and nq>5 The standard normal, since np5 and nq 5 O The Student's t, since np

Explanation / Answer

a) level of significance =0.05

Ho: p=0.092 ; Ha: p>0.092 ; right tailed

b)the standard normal since np>5 and nq>5

here std error =(p(1-p)/n)1/2 =0.021

sample proportion phat =27/190=0.1421

hence test statistic z=(phat-p)/std error =2.39

p value =0.0084

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