Question

A study was conducted to see whether monetary incentives to use less water during times of drought had an effect on water usage. Sixty single family homeowners were randomly assigned to one of two groups: 1) monetary incentives and 2) no monetary incentives. At the end of three months, the total amount of water usage for each household, in gallons, was measured.

(a) What would be the appropriate hypothesis test to use to test the claim that monetary incentives reduce water usage?

i. t-test for two independent samples

ii. t-test for dependent samples

iii. z-test for population mean

iv. correlation

(b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach?

Answer 1

a)

i. t-test for two independent samples is correct.

Expanation: It compares the two independent means when the knowledge of population variance is unknown. Here the two samples are independent and we do not know the variance of monetary incentives to use less water

ii. t-test for dependent samples is wrong

Explanation: It compares the two dependent means when the knowledge of population variance is unknown and two samples are dependent. The dependence of means mean the same subject is treated with two experiment.

iii. z-test for population mean is wrong

Expalantion: It compares the two means when the knowledge of population variance is known.

iv. correlation is wrong

Expalantion: Correlation analysis is a used to see the relationship between two sample. it doesnot tell about the difference between two sample means.

b)

The resaons for performing the t test for independent means

T test is used because we sare comparing two mean and we do not have prior knowledge of population variance

Independent samples is used beacuse the two samples means are independent of each other