Question

A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without

the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted.

Indicate if the hypothesis test is for

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

Short answer

The test is for matching or paired samples.

Step-by-step solution

Given information

A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without

the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted.

Calculation

Rain is simulated and 10 windshields are tested without the new treatment. Then the windshields are treated with the new treatment which claims to repel water better. Now the treated windshields are again tested with the same experiments.

Assuming mean of with and without new treatment sample difference is $\mu$.

The null and alternative hypothesis is given as :

$$\begin{gathered} {\mathrm{H}}_0:\mu =0 \\ {\mathrm{H}}_{\mathrm{a}}:\mu \ne 0 \end{gathered}$$

This shows that this hypothesis testis for matching or paired test.

Final answer

The test is for matching or paired samples.