Question

In the college population, the mean reading comprehension test score is  μ = 75 and σ = 25. A researcher wanted to investigate the effect of listening to hip-hop music on reading comprehension. She randomly selected a sample of n = 100 college students. The sample of students completed a reading comprehension test while hip-hop music was played in the background the sample mean reading comprehension score was M = 68.

Do the data indicate a significant effect of hip-hop music on reading comprehension? Use a two-tailed z - test with p < .05  to answer this research question.

- Null and alternative hypotheses

- All computational steps of the z-test

- Critical z-value used for decision about H₀

- Decision about H₀ (i.e., reject or fail to reject)

- If the effect is significant, compute the Cohen's d to establish the size of the effect - is the effect small, medium or large?

- Conclusion in APA style: interpretation of the z-test outcome to answer the research question. Is there a significant effect of hip-hop music on reading comprehension or not? If there is a significant effect, address in your conclusion the direction of the effect (i.e., is the effect positive or negative/is there an improvement or decline of reading comprehension?) and report the Cohen's effect size.

Please explain in very broken down and simple steps, thank you!

Answer 1

The Hypotheses are:

The rejection region:

Reject Ho if |Z|>Z_0.025 =1.96 calculated using Z table shown below

Test Statistic:

P-value:

P-value computed using Z score calculated above by using the Z table shown below as

P-value=0.0051

Decision:

Reject the null hypothesis.

Conclusion:

Since the P-value<<0.05 hence we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that mean has changed.

Cohen's D( Effect Size) is calculated as:

Cohen's d = (M_sample - µ_population) ⁄ σ

Cohen's d = (68 - 75) ⁄ 25 = 0.28.

Interpretation:

Since d=0.28 hence it has a small effect size.