A study was conducted to see whether monetary incentives to use less water durin

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?

Explanation / Answer

Solution.

a). The appropriate hypothesis test for given claim is

i. t-test for independent samples.

b). The t-test is is appropriate because of the following reasons.

Let mu1 be the average water usage in group 1 i.e. incentive group

And mu2 be the average water usage of group 2 i.e. no incentive group.

The hypothesis. Ho: there is no diddiffere between the water uses in the two groups.

Vs H1: the water usage of group 1 is less than group 2

OR

Ho: mu1=mu2

Vs . H1: mu1<mu2

And n (sample size) is 30 (<= 30) also population variance is unknown. With the two samples being independent and under the assumption that the parent population being normal. Fulfills all the assumption for the t test for two means . I.e. on tail t test .  

Under null hypothesis test statistics is t = (mu1-mu2)/(s/?n)

Follows students t distribution with 30+30-2=58 d.f.

And rejecte null hypothesis and accept the claim if t calculated < t tab at alpha level of significance with 58 d.f.

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