Question

For a study, 375 patients were randomly assigned tor eceive a daily dose of levvofloxacin, and 363 were given placebo. In the group receiving treatment, fever was present in 243 patients for the duration of neutroenia, whereas feverw as experienced by 308 patients in the placebo group. Using this information, determine whether or not the proportion of patients with fever differed between the two groups at the 1% level of significance. State the null and alternative hypothesis, manually calculate the test statistic and determine its p-value. Then state your decision and conclusion.

Answer 1

H₀: P1 = P2

H₁: P1 P2

= 243/375 = 0.648

= 308/363 = 0.848

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

                                                      = (0.648 * 375 + 0.848 * 363)/(375 + 363)

                                                      = 0.746

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

     = sqrt(0.746 * (1 - 0.746) * (1/375 + 1/363))

    = 0.0321

The test statistic z = ()/SE

                              = (0.648 - 0.848)/0.0321

                              = -6.23

P-value = P(Z < -6.23)

             = 0

Since the P-value is less than the significance level (0 < 0.01), so we should reject the null hypothesis.

So at 1% significance level, there is sufficient evidence to conclude that the proportion of patients with fever differed between the two groups.