a pharmaceutical company claims its new drug outperforms the

a pharmaceutical company claims its new drug outperforms the standard drug for combating the human immunodeficiency virus (HIV) . To support its claim, it has run an FDA-approved study treating 50 patients with the new drug and measuring their CD4, or T-cell counts (the higher, the better). The average CD4 count for patients treated with the standard drug is 500 cells/mmcubed. From the experiments, the empirical mean CD4 count is 516.28 cells/mmcubed, with a sampled standard deviation of 62.56 cells/mmcubed.

a) INspect the q-q plot from figure 1. Are the data normally distributed?

b) What is the approximate distribution of he sample mean? How do you know?

>t.test(CD4_dat,alternative = \'greater\' ,mu=500)

One Sample t-test

d) Whar is the Type I error rate for the test performed in part c?

e) If you performed the test in part c at 99% significance level, would the outcome be different? Why or why not?

f) If an experiment is repeated 100 times, and each time, a 75% confidence interval is created for the mean, how many time would you expect the true value of the mean to reside within the intervals?

Solution

We have given that

an FDA-approved study treating 50 patients with the new drug and measuring their CD4, or T-cell counts (n) = 50

average CD4 count for patients treated with the standard drug (µ0) = 500 cells/mmcubed.

the empirical mean CD4 count is (Xbar) = 516.28 cells/mmcubed,

sample standard deviation () =  62.56 cells/mmcubed.

INspect the q-q plot from figure 1. Are the data normally distributed?

From the normal q-q plot we can sya that the data is not normally distributed it is right skewed data.

b) What is the approximate distribution of he sample mean? How do you know?

The distribution of the sample mean is t-distribution because population standard deviation is unknown.