The table below shows the critical reading scores for 14 stu

The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At a=0.01, is there enough evidence to conclude that their scores improved the second time they took the test?

        1st      2nd
1      334   337
2      476   506
3      489   506
4      367   392
5      503   464
6      389   430
7      586   533
8      463   483
9      566   578
10   547   564
11   543   581
12   370   405
13   420   455
14   545   574

1. Identify the claim and state H0 and Ha

2. Find the critical values & identify the rejection regions.

3. Calculate d and s_d

4. Use the t-test to find the standardized the test statistic t

5. Decide whether to reject or fail to reject the null hypothesis

Solution

Let mu1 and mu2 represent the scores of students between the first and second time.

H0: mu1 = mu2

Ha: mu1<mu2

Left tailed test.

Difference Scores Calculations

Mean: 15
= 0
S² = SSdf = 10252(14-1) = 788.62
S²_M = S²N = 788.6214 = 56.33
S_M = S²_M = 56.33 = 7.51

T-value Calculation

t = (M - )S_M = (15 - 0)7.51 = 2.00

p = 0.9666

As p value is high, accept null hypothesis

There is no improvement as per statistical tests.