Question

Suppose a researcher is interested in a new treatment plan for CD4 cell count in immune-compromised patients with HIV. In order to investigate the new drug, the researcher gathers a group of 55 individuals with a mean CD4 count of 300 cells/mm3 after treatment with a standard deviation of 25.1. Test the hypothesis that the mean CD4 count goal is not 292 cells/mm3. Perform a two-way directional test, complete the 5 step process and calculate the appropriate confidence interval. (Use an alpha level of 0.01)

H0:u= (Example answer ###)

Ha:u ≠ (Example answer ###)

Ztest= (Example answer #.##)

p-value= (Example answer .###)

Confidence Interval= (Example answer ###.#,###.#)

Fail to reject or Reject the H0 (Example answer Fail to reject or Reject)

Answer 1

The Hypothesis

H0: = 292

Ha: 292

The Test Statistic:

The p Value:    The p value (2 Tail) for Z= ,is; p value = 0.0182

The Confidence interval

The Confidence Interval is given by ME, where

ME = Zcritical * \frac{\sigma}{\sqrt{n}} = 2.576 * \frac{25.1}{\sqrt{55}} = 8.72

The Lower Limit = 300 - 8.72 = 291.28

The Upper Limit = 300 + 8.72 = 308.72

The 99% Confidence Interval is (291.28 , 308.72)

The Decision: Since p value is > Alpha, and the value of 292 lies in the confidence interval, we fail to reject H0.