Question

Choose a variable that will allow the use of dependent samples. For example, you might wish to see if a persons’ proficiency at softball has changed/improved after a training camp. Do not use variables that are presented in the course in order to illustrate the concept. Select a sample of data (10 to 20) value pairs (e.g. before and after), and then complete the following:

e. State how the sample was selected.

f. Show the raw data in a table.

g. Decide which statistical test is appropriate and compute the test statistic (z or t). Why is the test appropriate?

h. Find the critical value(s).

Answer 1

A variable that will allow the use of dependent samples. : Consider a professor wants to test whether his lecture improves the performance of his students. He conducts a test both before his lecture and after his lecture. Hypothesis Test is to be done whether the improvement is scores ofstudents is significant.

(e) The sample was selected from the entire class by Simple Random Sampling using statistical methods.

(f)

A sample of data (10 to 20) value pairs (e.g. before and after), are got as follows:

x (Score before lecture)	y (score after lecture)
90	95
14	17
56	55
12	18
98	96
2	12
11	14
22	20
36	30
84	90
75	80
98	90
91	90
50	50

(g)

t test is appropriate because thepopulation standard deviation isnot given and sample size n =

Take =0.05

H0: 0 (The lecture is not effective)

HA: 0 (The lecture is effective) (Claim)

Values of d = Before - After are got as follows:

x (Score before lecture)	y (score after lecture)	d = X - Y
90	95	-5
14	17	-3
56	55	1
12	18	-6
98	96	2
2	12	-10
11	14	-3
22	20	2
36	30	6
84	90	-6
75	80	-5
98	90	8
91	90	1
50	50	0

From d values, the following statistics are calculated:

n = 14

= - 1.2857

sd = 5.0143

Test Statistic is given by:

(h)

df = 14 - 1 = 13

From Table, critical value of t = - 1.771

Since calculated value of t = - 0.959 is greater than critical value of t= - 1.771, reject null hypothesis.

Conclusion:
The data support theclaim that the lecture is effective.