Question

A study was performed to test the effectiveness of turmeric (a spice common in Indian and Indonesian cooking) in the treatment of knee arthritis.

There were 107 patients in the study. A random sample of 55 of these patients were placed in the “turmeric” group, and the remaining 52 in the “control” group. Patients in the control group received a standard treatment of Ibuprofen. All patients were timed going up and down a flight of stairs at the end of 6 weeks of treatment.

Patients in the turmeric group took an average of 24.8 seconds to go up and down the stairs, with an SD of 10.2 seconds. Patients in the control group took an average of 25.1 seconds, with an SD of 12.3 seconds.

We will construct a test to evaluate the null hypothesis that turmeric and Ibuprofen are equally effective, versus the alternative hypothesis that turmeric is more effective.

(a) Under the null hypothesis, the difference in the times is expected to be
 
 ________ seconds. The estimated standard error for the difference is ________ seconds.

(b) The two-sample z test statistic is __________.

(c) The p-value is approximately __________%.

(d) Our conclusion is to (circle one) reject the null hypothesis OR don’t reject the null hypothesis.

Answer 1

Answer:

a)

Given,

Null hypothesis Ho : u1 = u2

Alternative hypothesis Ha : u1 > u2

Under the null hypothesis, the difference in the times is expected to zero.

Standard error = sqrt(s1^2/n1 + s2^2/n2)

substitute values

= sqrt(10.2^2/55 + 12.3^2/52)

SE = 2.19

b)

test statistic z = (x1-x2)/se

substitute values

= (24.8 - 25.1)/2.19

z = - 0.14

c)

P value = P(z > - 0.14)

= 0.55567 [since from z table]

= 0.5557

P value = 55.57%

d)

Here we observe that p value > alpha(0.05), so we don't reject null hypothesis.