Question

Show your work. Carry out all calculations to at least 3 significant digits.

Marketing strategists like to study the differences (in, e.g., age and income) between buyers and non-buyers of a product. In an earlier study of the purchasers and non-purchasers of a product sold by the AAA Company, demographic data were collected. Their age profiles (in years) are summarized and reported as follows:

Purchasers
Sample size 900

Sample mean 43.8

Sample standard deviation 14.6

Non-Purchasers

Sample size 800

sample Mean 40.3

Sample standard deviation15.4

A. Based on the market demographic data obtained, do we have strong enough evidence to conclude that buyers of the company’s product are on average more than two years older than non-buyers are? Test using α = 0.05.

B. Construct a 95% confidence interval for the difference in average age between purchasers and non-purchasers of the product. Interpret the significance of the age difference.

Answer 1

Answer:-

Given That:-

Marketing strategists like to study the differences (in, e.g., age and income) between buyers and non-buyers of a product. In an earlier study of the purchasers and non-purchasers of a product sold by the AAA Company, demographic data were collected.

(a) We have find test statistic

Purchasers
Sample size 900

Sample mean 43.8

Sample standard deviation 14.6

Non-Purchasers

Sample size 800

sample Mean 40.3

Sample standard deviation 15.4

α = 0.05.

test statistic =

null hypothesis

Alternative hypothesis

Z = 2.054

(b) we have to find 95% confidence Interval

95% CI =   

95% CI Z_c = 1.645

= (3.5 - 1.2013), (3.5 + 1.2013)

95% CI = 2.299      4.701