Question

Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using this drug. It is hypothesized that regular exercise

might help reduce the headaches. If a random sample of 209 patients using diltiazem exercised regularly and only 16 had headaches, would this indicate a reduction in the population proportion of patients having headaches? Use a 1% level of significance.  

Answer 1

H0: p = 0.12

Ha: p < 0.12

Sample proportion = 16 / 209 = 0.0766

Test statistisc

z = - p / sqrt(p( 1 -p) / n)

= 0.0766 - 0.12 / sqrt(0.12 * 0.88 / 209)

= -1.93

This is test statistics value.

Critical value at 0.01 significance level = -2.326

Since test statistics > -2.326, we do not have sufficient evidence to reject H0.

p-value = P( Z < z)

= P( Z < -1.93)

= 1 - P( Z < 1.93)

= 1 - 0.9732

= 0.0268

p-value = 0.0268

p-value method= Since p-value > 0.01 level, we do not have sufficient evidence to reject H0.

We conclude at 0.01 level that we fail to support the claim.