Question

1Neutropenia. Neutropenia is an abnormally low number o neutrophils (a type of white blood cell) in the blood. Chemotherapy often reduces the number of neutrophils to a level that makes the patient susceptible to fever and infections. G. Bucaneve et al. published a study of such cancer patients in the paper "Levofloxacin to Prevent Bacterial Infection in Patients With Cancer and Neutropenia" (New England Journal of Medicine, Vol. 353, No, 10, pp. 977-987). For the study. 375 patients were randomly assigned to receive a daily dose of levofloxacin, and 363 were given a placebo. In the group receiving levofloxacin, fever was present in 243 patients for the duration of neutropenia, whereas fever was experienced by 308 patients in the placebo group.

a. At the1% significance level, do the data provide sufficient evidence to conclude that levofloxacin is effective in reducing the occurrence of fever in such patients?

b. Find a98% confidence level for the difference in the proportions of such cancer patients who would experience fever for the duration of neutropenia

Short answer

a) The data provide sufficient evidence to conclude that levofloxacin is effective in reducing the occurrence of fever in such patients.

b)There is 98% interval for the difference between the proportions is$(-0.2727,-0.1283)$

Step-by-step solution

Part(a) Step 1: Given Information

The given values are,

$$\begin{gathered} x_1=243, \\ {n}_1=375, \\ {x}_2=308, \\ {n}_2=363, \\ \alpha =0.01 \end{gathered}$$

Part(a) Step 2: Explanation

The null hypothesis.

$H_0:p_1=p_2$

The alternative hypothesis.

$H_a:p_1<p_2$

Using MINITAB output.

MINITAB output: Test and Cl two proportions

From the MINITAB, the test statistic is $-6.26$and the $p$- value is $0.000$.

$p$- value is lesser than the level of significance.

$p\text{- value}(=0.000)<\alpha (=0.01)$

Using the rejection rule, it can be concluded that there is evidence to reject the null hypothesis $H_0$at $\alpha =0.001$. Therefore, the data provide sufficient evidence to conclude that levofloxacin is effective in reducing the occurrence of fever in such patients.

Part (b) Step 1: Given Information

The given values are,

$$\begin{gathered} x_1=243, \\ {n}_1=375, \\ {x}_2=308, \\ {n}_2=363, \\ \alpha =0.01 \end{gathered}$$

Part(b) Step 2: Explanation

Using MINITAB output.

Using the MINITAB output.

MINITAB output: Test and CL for two proportions

From the MINITAB output,$98\%$ confidence interval is $(-0.2727,-0.1283)$

Therefore, there is$98\%$ confidence interval for the difference between the proportion is $(-0.2727,-0.1283)$.