Question

3. A teacher believes that a new method will improve students’ reading ability. For 8 weeks, she teaches a class of 21 students using these new methods. Meanwhile a colleague uses “traditional” methods to teach his 23 students. At the end of the 8 weeks, all the students are given the Degree of Reading Power Test. Here are the scores:

         New Method students

24	43	58	71	43	49
61	44	67	49	53	56
59	52	62	54	57	33
46	43	57

Traditional Method students

42	43	55	26	62
37	33	41	19	54
20	85	46	10	17
60	53	42	37	42
55	28	48

Are we justified in using the t procedures? Explain.

Give a significance test to check the teacher’s theory. Include all relevant components. (you may wish to list some “background” items first)

Give a 99% confidence interval for the mean difference between the two groups of students

Draw an overall conclusion based on parts B and C.

Answer 1

a) To use t procedures for sample size of atleat 15 there should not be a strong skewness in the data.

If skewness is < -1 and > 1 skewness is strong.

Skewness = where is the mean of sample is the observation.

S.No	News Method	Traditional Method
1	24	10
2	33	17
3	43	19
4	43	20
5	43	26
6	44	28
7	46	33
8	49	37
9	49	37
10	52	41
11	53	42
12	54	42
13	56	42
14	57	43
15	57	46
16	58	48
17	59	53
18	61	54
19	62	55
20	67	55
21	71	60
22		62
23		85

Skewness of new method = -0.626 moderate skewness

Skewness of tradional method = 0.309 approximately symmetric

Since there is no strong skewness in both of the datasets we can use t procedures.

b) Hypothesis

where is the population mean for new method

is the population mean for traditional method

Assuming equal variances of the population i.e., and %

test statistic t₀

for the given data
  

  

        

for t₀ = 2.265 and 42 degrees of freedom P - Value = 0.014 hence reject null hypothesis.

c) 99% confidence interval

t_0.05,42 = 1.682

Substituing the values

d) Since the null hypothesis ie rejected test is statistically significant. The CI does not contain zero and the range is greater than zero hence from this we can conclude that new method of teaching is better than traditional method of teaching.