Suppose the manufacturer of Advil, a common headache remedy, recently developed

Question

Suppose the manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a sample of 260 current users is asked to try it. After a one-month trial, 244 indicated the new drug was more effective in relieving a headache. At the same time a sample of 360 current Advil users is given the current drug but told it is the new formulation. From this group, 322 said it was an improvement. (1) State the decision rule for .02 significance level: H0: ?n ? ?c; H1: ?n > ?c. (Round your answer to 2 decimal places.) Reject H0 if z > (2) Compute the value of the test statistic. (Do not round the intermediate value. Round your answer to 2 decimal places.) Value of the test statistic (3) Can we conclude that the new drug is more effective? Use the .02 significance level. H0. We conclude that the new drug is more effective.

Explanation / Answer

H0: P1 = P2

H1: P1 > P2

p1 = 244/260 = 0.938

p2 = 322/360 = 0.894

The pooled proportion (P) = (p1 * n1 + p2 * n2)/(n1 + n2)

                                          = (0.938 * 260 + 0.894 * 360)/(260 + 360)

                                          = 0.91

SE = sqrt(P * (1 - P) * (1/n1 + 1/n2)

     = sqrt(0.91 * (1 - 0.91) * (1/260 + 1/360))

    = 0.023

THe test statistic z = (p1 - p2)/SE

                              = (0.938 - 0.894)/0.023

                              = 1.91

P-value = P(Z > 1.91)

             = 1 - P(Z < 1.91)

             = 1 - 0.9719

             = 0.0281

As the P-value is greater thab the significance level (0.0281 > 0.02), so the null hypothesis is not rejected.

So do not reject H0. We cannot conclude that the new drug is more effective.

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