Question

The spreadsheet titled "Test Scores" shows the reading and writing scores a sample of 12 students earned on a standardized test. Assuming normal distributions and using an alpha level of .05, conduct the appropriate test to see if there is a significant difference between the population mean for the reading scores and the population mean for the writing scores.

Student	Reading Score	Writing Score
1	448	308
2	598	593
3	527	430
4	582	448
5	589	393
6	316	615
7	624	472
8	569	438
9	360	381
10	564	307
11	508	338
12	625	443

Answer 1

Let us denote

d : reading score - writing score

To test against

Here

sample mean of difference

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic =

and P-value =

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that there is a significant difference between the population mean for the reading scores and the population mean for the writing scores.