A researcher wants to find out who plays with their dogs more, people who live i

Question

A researcher wants to find out who plays with their dogs more, people who live in a big city or people who live in the suburbs. She asked 17 city dwelling dog owners and 21 suburb dwellers how many minutes per week they actively play with their dogs. The sample mean for city dwellers was found to be 113 minutes with a sample standard deviation of 7. The sample mean for those in the suburbs was 104 with a sample standard deviation of 12. You have evidence that allows you to assume the population variances are equal. Can we say that city dwellers play with their dogs more than those who live in the suburbs at the .05 level of significance? Show all 5 steps and interpret your results.

Explanation / Answer

Null Hypothesis H0 : mu1 < = mu2

Alternate Hypothesis Ha : mu1 > mu2

n1 = 17 , n2 = 21 , s1 = 7 , s2 = 12 , x1 = 113 , x2 = 104

Test statistic:

t = (x1 - x2) / sp *sqrt ( 1/n1 + 1/n2)

We need to find sp

Sp = sqrt ((n1 -1) *s1^2 + (n2 - 1) * s2^2/(n1+n2-2))

= sqrt (( 17 - 1) * 7^2 + (21-1) * 12^2 / ( 17 + 21 -2))

= 10.08

t = (113 - 104 ) / 10.08 * sqrt ( 1/ 17 + 1/21)

= 2.73

now, we need to dind degree of freedom = n1+n2 -2 = 17 +21 - 2 = 36

Find p value using t statistic value and df So, we get the p value = 0.0048

Now, alpha = .05 And p value = 0.0048 So, p value < .05

So, we reject the null Hypothesis

Yes, we can say that city dwellers play with their dogs more than those who live in suburbs.

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