Ackerman & Goldsmith (2011) found that students who studied text from printed hard copy had better test scores than students who studied text presented on a screen. In a related study, a professor noticed that several students in a large class had purchased the e-book version of the course textbook. For the final exam, the overall average for the entire class was μ = 85, but the n = 10 students who purchased the e-book had a mean of M = 77 with a standard deviation of s = 6. Do these data indicate a significant decrease in test scores on the final exam due to the use of a e-book? Use a one-tailed test with α = .05.

To test this, a professor took a sample of 10 students that purchased the ebook version of the materials to compare it to the overall class information.

Historically the average scores of the class are μ=85

Sample information is:

n=10

sample mean, X[bar]= 77

sample standard deviation S= 6

The hypothesis is:

H₀: μ ≥ 85

H₁: μ < 85

α: 0.05

Z= X[bar] - μ ≈ N(0;1)

S/√n

Since we don't have information about the variable distribution, but the sample is big enough, applying CLT I've approximated the distribution of the sample mean to normal. That's why the statistic is a Z.

The critical value is

[tex]Z_{alpha } = Z_{0.05} = -1.64[/tex]

You'll reject the null hypothesis if the calculated Z value ≤ -1.64 and support it if Z > -1.64.

Z[tex]_{H0}[/tex]= (77 - 85)/(6/√10) = -4.216

Since the calculated value is less than the critical value, you reject the null hypothesis.

This means, that there is a significant decrease in the test scores of the final exam due to the use of the e-book.

I hope it helps!