Is it a good idea to listen to music when studying for a final exam test? Does it matter what music you listen to? A researcher conducted a study. He worked with two independent samples, a randomsample 1of 48 students who were asked to listen to music by Beethoven and another randomsample 2of 105 students who were asked to listen to Hip-Hop music while attempting to memorize objects pictured on a page. They were then asked to list all the objects they could remember (memory score). Here are the summary statistics for each group: the sample means arex1=10.3x1=10.3for sample 1 andx2=9.3x2=9.3for sample 2. Suppose that the population standard deviations are1=1.51=1.5and2=1.82=1.8are available. Could the researcher claim at a 1% level of significance that on average, there is no significant difference in memory score depending on the type of music students listen to? Use thezz-test for two independent samples and the formula,

zst=(x1x2)(12)21n1+22n2

(a) State the null and alternative hypotheses, and identify which one is the claim. H0H0: Select an answer: - - x x - x x - choose one: > < = H1H1: Select an answer: x - - x - x - x choose one: > = < Which one is the claim?

• H0
• H1

(b) Find the critical value(s). In the first box please indicate the sign(s), and in the second box enter the numeric value.

Use the following table ofzvaluesfor most commonvalues.

	0.005	0.01	0.02	0.03	0.04	0.05	0.06	0.1
zz	2.575	2.33	2.05	1.88	1.75	1.645	1.555	1.28
z2z2	2.81	2.575	2.33	2.17	2.05	1.96	1.88	1.645

Critical Value(s) = choose one: + ans:____ (c) What is the test statistic?

Use the correct sign for the test statistic and round your answer to 3 decimal places.

zst=

(d) Does the test statistic fall into rejection region? Yes or No (e) What is the short version of your conclusion (in terms ofH0andH1)?

• SupportH0H0and fail to rejectH1H1(claim)
• RejectH0H0and fail to supportH1H1(claim)
• Fail to supportH0H0and rejectH1H1(claim)
• Fail to rejectH0H0(claim) and fail to supportH1H1
• RejectH0H0(claim) and supportH1H1

(f) Select the correct statement.

• At a 1% level of significance, there is sufficient evidence to warrant rejection of the claim that on average, there is no significant difference in memory scores of students who listen to music by Beethoven and students who prefer Hip-Hop music.
• I proved that the average memory score of students who listen to music by Beethoven is lower than the average memory score of students who listen to Hip-Hop music.
• At a 1% level of significance, there is not sufficient evidence to warrant rejection of the claim that on average, there is no significant difference in memory scores of students who listen to music by Beethoven and students who prefer Hip-Hop music.
• I have an evidence that the average memory score of students who listen to music by Beethoven is higher than the average memory score of students who prefer Hip-Hop music.