Question

1. A random sample of 25 inpatients in a hospital had a mean healthcare expenditure of $2000 and standard deviation of $300. Use these values to test the following hypotheses at α = 0.01:

   1. (a) whether or not the mean healthcare expenditure among all inpatients in the hospital is less than $2300.

   2. (b) whether or not the mean healthcare expenditure among all inpatients in the hospital is different from $2100.

1. A medical researcher is testing a new drug to see if it slows the growth of malignant tumors in rats. The control group of 20 rats is given non of the drug and the test group of 15 rats is given a dose every day for two weeks. At the end of the test, the following statistics were calculated from the samples:

Table 1:
Control rats

Average growth of tumor 6 grams Standard deviation 3 grams

Test rats 4 grams 2 grams

  

Given the assumption that the variances of the two population are equal, conduct the appropriate hypothesis test to determine if the new drug appears to slow the mean rate of tumor growth at α = 0.05.

Answer 1

n=25 X = 2000 s= 300 2=0.01 Ho: Hi to = 23,00 u < 2300 Cayt Tailed) x-4 Ntn 1 - 1 Tin 2000 - 2300 = -5 = 300/25 Critical Ance Mean tool, 24 = -2.492 t <-2.492 We Reject Ho re- health care expendilaus is less than 2300. Ho 4= 2 100 HI M = 2100 t= x -4 = 2000- 2100 = -1.667 300/ES Ite 1.667 buitical to 01, 24: 2.797 Since + <2.797 We do not reject to e mean Health care expenditure is not different from 2100 - Ho Drug has no effect I e l, = M₂ HI: 1) Drug slow the mean Rate of Tummor quouthie. HI U2 *-* N thith-2 , w thitm-2 ī steno cno ]$?+ (m2=18227 - H - 22° 1 - t 52 t = critical 1 (19) (3) + (14) (2 3² 7 = 6-4 //2.6227 5/20+ Ys] = t33 0.05= 1.69 7 1.69 Reject rate of Tumuor 6.8787 [2.2326 = 2.6227 . since Ho so errourth Drug slow the mean