Question

The following are the number of sales which a sample of 9 car salespeople of an insurance company in Florida and a sample of 8 salespeople in Washington made over a certain year. Florida: 39, 44, 42, 50, 55, 48, 51, 38, 54 Washington: 42, 43, 56, 50, 49, 52, 53, 56 Assuming that the populations sampled can be approximated closely with normal distributions having the same variance, is there a difference in the number of sales between the Florida salespeople and the Washington salespeople?

Find s^2p (round off to the nearest integer)

Answer 1

There is no difference in the number of sales between The Florida salespeople and Washington salespeople

Sp^2 = 39

Explanation:

Given data :

Florida: 39, 44, 42, 50, 55, 48, 51, 38, 54

Washington: 42, 43, 56, 50, 49, 52, 53, 56

number of sales persons in Florida = 9

number of sales persons in Washington = 8

variance = constant

a)Determine if there is difference between the Florida salespeople and Washington salespeople

we will carry out a two tailed test based on the given data

H0 : u1 = u2

H1 : u1 ≠ u2

x ( mean ) = 46.77, y ( mean ) = 50.13 ,

s1^2 = 39.69, s2^2 = 28.41, n1 = 9 , n2 = 8

therefore :

Sp^2 =
`(n1s1^2 + n2s2^2)/(n1 + n2-2)` = 38.96 ≈ 39

performing test statistic

t =
`\frac{x- y }{sp\sqrt{(1)/(n1) +(1)/(n2) } }` =
`(-3.36)/(3.0330)` = -1.1078

critical value is at t = 0.05 and for a two tailed test it is at 2.13 therefore e accept H0 at 5% . This shows that there is no difference in sales