Question

A town is trying to determine if a new recycelin incentive would increase the number of people thatseperate their garbage from recycable iems. to make this determination a simple random sample of 10 streets and the number of people that recycle on these streets is countedonce before and once after the recycling incentive has been intitated. the date shows a mean difference of3.78 and a standard deviation of 1.33.

Required:
Determie if the recycling incentive was effectiive with a 5% significnc level.

Answer 1

The recycling incentive was effective at 5% significance level.

Explanation:

The null and alternative hypothesis are

H0 u1≤ u2 against the claim Ha: u1> u2

or

H0 ud=0 against the claim Ha: ud > 0

The significance level is ∝=0.05

Data given

d`= 3.78

sd= 1.33

n= 10

The test statistic is

t= d`/ sd/ √n

t= 3.78/1.33/√10

t= 9.3889

The critical region for ∝=0.05 and df.= (n-1)= 9 is t> 1.833

Since the calculated value of t lies in the critical region it is concluded that new recycling incentive would increase the number of people that seperate their garbage from recyclable items.

H0 is rejected and Ha is accepted.