Question

6) The table below represents data on a variable of interest collected from a single sample measured at two different points in time. A researcher is interested in testing whether scores are higher at the second measurements.
Time 1 8 6 7 5 2 8 9 3 4 7

Time 2 7 9 11  6 4 5 8 7 4 5

a) What are the appropriate hypotheses for this analysis? b) What is/are the critical value(s) for this test at a 0.05 alpha level? c) What is the estimated standard error for this test? d) What is the observed value of the appropriate test statistic? e) What is your decision regarding the stated hypotheses?

Answer 1

Given :

The table below represents data on a variable of interest collected from a single sample measured at two different points in time.

Time 1 : 8 6 7 5 2 8 9 3 4 7

Time 2 : 7 9 11  6 4 5 8 7 4 5

Table for calculating mean and standard deviation :

Time 1 (X)	Time 2 (Y)	d = X-Y	d^2
8	7	1	1
6	9	-3	9
7	11	-4	16
5	6	-1	1
2	4	-2	4
8	5	3	9
9	8	1	1
3	7	-4	16
4	4	0	0
7	5	2	4
		d = -7	d^2 = 61

a) Hypothesis test :

The null and alternative hypothesis is

Ho : d = 0

Ha : d > 0

b) The critical value(s) for this test at a 0.05 alpha level :

Degree of freedom = df = n-1 = 10-1 = 9

At 0.05 significance level the critical value of t is

Dicision : Fail to reject (do not reject) the null hypothesis.

Conclusion : The is not sufficient evidence to conclude that the scores are higher at the second measurement.