Question

psychological test before and after treatment in order to determine the effectiveness of the treatment. Researchers hope to find a difference in test scores before and after treatment. A 95% CI for the population average difference in test scores (before-after) is given by (0.25, 3.75), which was computed based on a random sample of 36 patients.

a) What is the population parameter of interest? mu1? mu2? mud?

b) Based on the confidence interval, at a 5% significance level, would 0 be considered a reasonable value of the population parameter?

c) Based on the CI, what is the value of the sample statistic (point estimate)?

d) Based on the CI and the sample statistics found in c). What is the value of the standard error (SE) of the sample statistic? Hint: UB = point estimate + margin of error = Xd+E= Xd+cv X SE(Xd)

e) Is there a significant difference in test scores (before - after) on average? Perform an appropriate hypothesis test using α = 0.10.

I. List data assumptions.

II. State H0 and Ha.

III. Calculate the test statistic.

IV. Make decision using the rejection region approach.

V. Draw conclusion.

Answer 1

Given ;

95% CI for the population average difference in test scores (before-after) is given by (0.25, 3.75)

Sample size = n = 36

a) The population parameter of interest mud (d)

b)Yes, based on the confidence interval, at a 5% significance level, 0 would be considered a reasonable value of the population parameter.

c) Based on the CI, The value of the sample statistic (point estimate) is

Point estimate = (upper limit + lower limit )/2 = (0.25+3.75)/2 = 4/2 = 2

d) The value of the standard error (SE) of the sample statistic is

Margin of error = (upper limit-lower limit)/2 = (3.75-0.25)/2 = 1.75

Standard error = Margin of error/Z/2 = 1.75/1.96 = 0.892

e)

Since P-value is less than significance level 0.05, we reject the null hypothesis.

Conclusion : There is a significant difference in test scores (before - after) on average.