Question

This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using the drug. It is hypothesized that regular exercise might help reduce the headaches. If a random sample of 212 patients using diltiazem exercised regularly and only 19 had headaches, would this indicate a reduction in the population proportion of patients having headaches? Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

(b) What sampling distribution will you use? The standard normal, since np > 5 and nq > 5. The Student's t, since np > 5 and nq > 5. The Student's t, since np < 5 and nq < 5. The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answers to two decimal places.)

(c) Find the P-value of the test statistic. (Round your answers to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the true proportion of patients having headaches is less than 12%. There is insufficient evidence at the 0.01 level to conclude that the true proportion of patients having headaches is less than 12%

Answer 1

n = 212

x = 19

Claim:The true proportion of patients having headaches is less than 12%

a)   level of significance

Null and alternative hypothesis is

Ho : p = 0.12

H1: p < 0.12

Level of significance = 0.01

b) The standard normal, since np > 5 and nq > 5

Test statistic is

c)

P-value = P(Z <-1.36) = 0.0869 ( Using z table)

P-value = 0.0869

  P-value , Failed to Reject Ho

d)

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

e)

There is insufficient evidence at the 0.01 level to conclude that the true proportion of patients having headaches is less than 12%