Question

A study had subjects read a passage and take a comprehension test on what they read. The researchers randomly assigned subjects so that half of them listened to music with lyrics while reading, while the other half listened to music without lyrics while reading. Here are their scores on the comprehension test: Music with lyrics 75 62 65 41 54 Music without lyrics 64 71 88 77 62 The researchers want to test if these results represent a significant difference in the average score between the groups. Assume that the necessary conditions for inference were met. Which of these is the most appropriate test and alternative hypothesis?

Answer 1

two-sample t test with Ha: ulyrics ≠ uwithout

Explanation:

Answer 2

Ha: ud≠0

The test statistic is

t= d`/ sd/ √n

Explanation:

The null and alternate hypothesis are

H0: these results do not represent a significant difference in the average score between the groups

H0: ud= 0

against the claim

Ha: these results represent a significant difference in the average score between the groups

Ha: ud≠0

The test statistic is

t= d`/ sd/ √n

where d` is the mean of the difference between the groups

sd is the standard deviation of the difference between the groups

and n is the number of observations.

d`= ∑di/n

sd= ∑(di- d`)²/n-1

When the observations from two samples are paired either naturally or by design we find the difference between two observations of each pair. Treating the differences as a random sample from a normal population with mean ud= u1- u2 and unksnown standard deviation σd, we perform one sample t -test on them. This is called paired difference t test or a paired t- test.