Question

You wish to determine if teaching statistics with definitional formulas changes students’ conceptual understanding of psychological statistics. We know the average performance on a national statistics exam (µ = 65). Thus, a sample of students (n = 8) were taught statistics with only definitional formulas. After the class ended, all 8 students took a national statistics exam. Their scores are listed below:

68, 69, 92, 77, 71, 99, 82, 74

Therefore, the research hypothesis is that teaching with definitional formulas changes students’ conceptual understanding of psychological statistics.

Answer 1

From the sample data

= 79 , S = 11.2884

The null and alternative hypothesis are

H0: = 65

Ha: 65

Test statistics

t = - / (S / sqrt(n)

= (79 - 65) / ( 11.2884 / sqrt(8) )

= 3.51

t critical value at 0.05 level with 7 df = -2.365 , 2.365

Since test statistics falls in rejection region , Reject H0.

We conclude at 0.05 level that we have sufficient evidence to support the claim.