Question

A study was conducted comparing muscle function between patients with RA and OA. A 10 point scale was used to assess balance and coordination in which a high score indicates a better coordination. There were 36 RA patients. 30 OA patients. The RA mean balance score was 3.4 and the OA mean balance score was 2.5. The RA standard deviation is 3.0 and the OA standard deviation is 2.8. What is the best estimate of the proportion of RA and OA patients with impaired balance where impaired balance is defined as a balance score of less than or equal to 2 and normality is assumed. Sketch the distribution and show evidence of how you got estimate.

Answer 1

The proportion of RA patients with impaired balance

Let the random variable, X = balance score

The sample distribution of random variable X follows a normal distribution with

sample mean = 3.4

sample standard deviation = 3

sample size = 36

Since the population standard deviation is not known, the proportion of RA patients with mean balance score less than or equal to 2 is obtained by calculating the t score as shown below,

The p-value is obtained in excel using the function =T.DIST(-2.8,35,TRUE) for degree of freedom = n-1=35.

Hence, the proportion of RA patients with an impaired balance is approximately 0.0041

The distribution is sketched in free online software StatKey by following these steps,

Step 1: Go the Starkey > Theoretical Distribution > T distribution > OK

Step 2: Degree of freedom = 35.

Step 3: Select Left Tail > Edit T value = -2.8.

The screenshot is shown below,

The proportion of OA patients with impaired balance

Let the random variable, X = balance score

The sample distribution of random variable X follows a normal distribution with

sample mean = 2.5

sample standard deviation = 2.8

sample size = 30

Since the population standard deviation is not known, the proportion of OA patients with mean balance score less than or equal to 2 is obtained by calculating the t score as shown below,

The p-value is obtained in excel using the function =T.DIST(-0.97808,35,TRUE) for degree of freedom = n-1=29.

Hence, the proportion of OA patients with an impaired balance is approximately 0.1681

The distribution is sketched in free online software StatKey by following these steps,

Step 1: Go the Starkey > Theoretical Distribution > T distribution > OK

Step 2: Degree of freedom = 29.

Step 3: Select Left Tail > Edit T value = -0.97808.

The screenshot is shown below,