Question

A publishing company wanted to test whether typing speed differs when using word processor A or word processor B. A random sample of 25 typists was selected and the typing speeds (in words per minute) were recorded for each typist when using word processor A and then when using word processor B. (Which word processor is used first is determined for each secretary by a coin flip). In this case, which of the following is the appropriate set of hypotheses?

a. (H0: μ = 0) and (Ha: μ ≠ 0)
b. (H0: μ = 0) and (Ha: μ > 0)
c. (H0: μ = 0) and (Ha: μ < 0)
d. None of the above. This is not a matched pairs situation.

Answer 1

Option d : None of the above. This is not a matched pairs situation.

Explanation:

We are given that a publishing company wanted to test whether typing speed differs when using word processor A or word processor B.

A random sample of 25 typists was selected and the typing speeds (in words per minute) were recorded for each typist when using word processor A and then when using word processor B.

The above situation suggests that this is situation of Paired data {Dependent limits} hypothesis because as we can see that the 25 typists which are used for checking their typing speed using word processor A are same as that of typists that are used for checking typing speed using word processor B.

This means that both situations are taken from the same sample; there are not any independent samples.

So, the correct hypothesis that would be used here is;

Null Hypothesis,
`H_0` :
`\mu_d` = 0 {means that the typing speed remains same when using word processor A or word processor B}

Alternate Hypothesis,
`\mu_d\\eq` 0 {means that the typing speed differs when using word processor A or word processor B}

Hence, option d would be apt for this situation.