Question

5. In a pediatric clinic a study was carried out to see how effective acetaminophen is in re- ducing temperature. Seven 5 year old children suffering from influenza had their tem- peratures taken immediately before and 1 hour after administration of acetaminophen. The results were: Patient Before After 102.4 99.6 103.2 100.1 101.9 100.2 103 101.1 101.2 99.8 100.7 100.2 102.5 101.0 (a) Use a test based on the normal assumption to determine whether the acetaminophen is effective in reducing temperature. i. State the hypotheses. ii. Evaluate the test statistic. iii. Calculate the P value. iv. Draw a conclusion in the context of the problem. V. Are the results statistically significant at the α .05 level? (b) Construct a 99% confidence interval for the difference in rneans

Answer 1

a) i) Two paired t-test:

patient	Before	After	Diff
1	102.4	100	3
2	103.2	100.1	3
3	101.9	100.2	2
4	103	101.1	2
5	101.2	99.8	1
6	100.7	100.2	1
7	102.5	101	2
Mean	102.13	100.2857	1.842857
Std	0.9196	0.566947	0.879123

$H_0:\mu _d=0$ and $H_a:\mu _d>0$

Test statistic:

$t= \frac{\bar{d}}{s/\sqrt{n}}= \frac{1.842857}{0.879123/\sqrt{7}}=5.546143$

P-value: 0.001

The test statistic is significant and rejects H0. There is evidence to support the claim.

b) 99% confidence interval:

df= n-1= 6

$\bar{d}\pm t_{df,\alpha /2}*\frac{s}{\sqrt{n}}=> 1.842857\pm 3.707*(\frac{0.879123}{\sqrt{6}})$

Lower limit: $1.842857- 1.231752=0.611105$

Upper limit: $1.842857+ 1.231752=3.074609$