Question

8. One of the eff e purposes of an investigati on by Porcellini et al. was to investigate the ect of CD4 T cell count of administration of intermittent interleukin IL-2 addition to highly active antiretroviral therapy (HAART). The shows the CD4 T cell count at baseline and then again after 12 months up of HAART therapy with IL-2 in following table of follow- CD4 T cell count atCD4 T cell count at the baseline (x10/L) end of follow-up (x109/L) 257 2 3 4. 5 6 7 173 58 103 181 105 301 169 108 315 362 141 549 369 Do the data show, at the 0.05 level, a significant change in CD4 T cell count? Sate your null and alternative hypotheses. Additionally, please enter the data into STATA (special way) and perform the same test using STATA (6+5+2+5 points).

Answer 1

Answer:

baseline	followup	difference
173	257	-84
58	108	-50
103	315	-212
181	362	-181
105	141	-36
301	549	-248
169	369	-200

Descriptive statistics
	difference
count	7
mean	-144.4286
sample standard deviation	85.6774
sample variance	7,340.6190

Paired t test

Null hypothesisH0·Ha = 0 Alternative hypothesis : H1 : Hat 0

Two tailed test used

Sd

144.4286 85.6774/V7

= -4.46

DF = n-1 =6

Table value of t with 6 DF at 0.05 level =2.4469

Rejection Region: Reject Ho if t < -2.4469 or t > 2.4469

Calculated t = -4.46 falls in the rejection region

The null hypothesis is rejected.

We conclude that there is a significant change in CD4 T cell count.

Stata output:

ttest Baseline == followup

Paired t test

------------------------------------------------------------------------------

Variable |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]

---------+--------------------------------------------------------------------

Baseline |       7    155.7143    29.72951    78.65688     82.9688    228.4598

followup |       7    300.1429    56.65788    149.9027     161.506    438.7797

---------+--------------------------------------------------------------------

    diff |       7   -144.4286    32.38302    85.67741    -223.667   -65.19018

------------------------------------------------------------------------------

     mean(diff) = mean(Baseline - followup)                       t = -4.4600

Ho: mean(diff) = 0                              degrees of freedom =        6

Ha: mean(diff) < 0           Ha: mean(diff) != 0           Ha: mean(diff) > 0

Pr(T < t) = 0.0021         Pr(|T| > |t|) = 0.0043          Pr(T > t) = 0.9979

.

Calculated t= -4.46, P=0.0043 which is < 0.05 level. Ho is rejected.