Question

1. A study was conducted comparing muscle function between patients with rheumatoid arthritis (RA) and osteoarthritis (OA). A 10-point scale was used to assess balance and coordination where a high score indicates better coordination. Results are below. Assume that the population distribution of the score is normal, but the variances of the two populations are not equal. 3.4 OA 30 2.5 a) Conduct a two-sided test at the 0.05 level of significance to determine whether there is a difference in muscle function when comparing patients with RA versus OA. Report a p- value. b) What are the assumptions that must be met for this test to be valid?

Answer 1

A ) let the null and alternative hypothesis is

$Ho:\mu _{RA}= \mu _{OA}$

$Ho:\mu _{RA}\neq \mu _{OA}$ (Two-tailed test)

using minitab>stat>basic stat>two sample t test

we have

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 36 3.40 3.00 0.50
2 30 2.500 0.900 0.16

Difference = μ (1) - μ (2)
Estimate for difference: 0.900
95% CI for difference: (-0.162, 1.962)
T-Test of difference = 0 (vs ≠): T-Value = 1.71 P-Value = 0.095 DF = 42

p value = 0.095

since p value is greater than 0.05 so we will accept H0 and conclud that there is no difference between the patients with RA and OA.

b ) the assumption which must be satisfied are

the samples should be independent of each other

data should come from normally distributed population