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 196 donors, it is found that 29 have hypertension. Do these data indicate that the population proportion of students with hypertension during final exams week is higher than 9.2%? se a 5% level of significance.

Explanation / Answer

here null hypothesis: p<=0.092

alternate hypothesis: p>0.092

for 0.05 level critical value =1.645

std error =(p(1-p)/n)1/2 =0.02

phat=29/196=0.148

hence test stat z=(phat-p)/std error =(0.148-0.092)/0.02=2.7106

as test stat is higher then critical value; we reject null hypothesis and conclude that hypertension during final week is higher then 9.2%

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