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 random sample 1 of 44 students who were asked to listen to music by Mozart and another random sample 2 of 97 students who were asked to listen to Pop 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 are ¯x1=10.5x¯1=10.5 for sample 1 and ¯x2=9.5x¯2=9.5 for sample 2. Suppose that the population standard deviations are σ1=1.5σ1=1.5 and σ2=1.8σ2=1.8 are available. Could the researcher claim at a 4% level of significance that on average, there is no significant difference in memory score depending on the type of music students listen to? Use the zz-test for two independent samples and the formula,
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 random sample 1 of 44 students who were asked to listen to music by Mozart and another random sample 2 of 97 students who were asked to listen to Pop 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 are ¯x1=10.5x¯1=10.5 for sample 1 and ¯x2=9.5x¯2=9.5 for sample 2. Suppose that the population standard deviations are σ1=1.5σ1=1.5 and σ2=1.8σ2=1.8 are available. Could the researcher claim at a 4% level of significance that on average, there is no significant difference in memory score depending on the type of music students listen to? Use the zz-test for two independent samples and the formula,
zst=(¯x1−¯x2)−(μ1−μ2)√σ21n1+σ22n2zst=(x¯1-x¯2)-(μ1-μ2)σ12n1+σ22n2
(a) State the null and alternative hypotheses, and identify which one is the claim.
H0H0:
H1H1:
Which one is the claim?
- H1H1
- H0H0
(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 of z values for most common αα values.
| αα | 0.005 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.1 |
|---|---|---|---|---|---|---|---|---|
| zαzα | 2.575 | 2.33 | 2.05 | 1.88 | 1.75 | 1.645 | 1.555 | 1.28 |
| zα2zα2 | 2.81 | 2.575 | 2.33 | 2.17 | 2.05 | 1.96 | 1.88 | 1.645 |
Critical Value(s) =
(c) What is the test statistic?
Use the correct sign for the test statistic and round your answer to 3 decimal places.
zst=zst=
(d) Does the test statistic fall into rejection region?
(e) What is the short version of your conclusion (in terms of H0H0 and H1H1)?
- Reject H0H0 and fail to support H1H1 (claim)
- Support H0H0 and support H1H1 (claim)
- Fail to reject H0H0 (claim) and fail to support H1H1
- Fail to support H0H0 and reject H1H1 (claim)
- Reject H0H0 (claim) and support H1H1
(f) Select the correct statement.
- I proved that the average memory score of students who listen to music by Mozart is lower than the average memory score of students who listen to Pop music.
- At a 4% 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 Mozart and students who prefer Pop music.
- At a 4% 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 Mozart and students who prefer Pop music.
- I have an evidence that the average memory score of students who listen to music by Mozart is higher than the average memory score of students who prefer Pop music.
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