Question

An online survey company wants to know if customer age is important in deciding to subscribe. The company has gathered a random sample of 1000 people from the population and asked each person whether he or she would subscribe to a service. Perform all the steps of a hypothesis test with a = 0.05 to determine whether or not an individual would subscribe to a service and age are independent.

Age
Under 18 18-34 35 and Over Total
Yes 120 262 237 619
No 41 103 237 381
Total 161 365 574 1000

Answer 1

service subscription and age are not independent

Explanation:

The appropriate statistical test to adopt for the above problem is the Chisquare test.

The hypothesis :

H0 : service subscription and age are independent

H1 : service subscription and age are not independent

Observed values :

Under 18 18-34 35 and Over Total

Yes__ 120 __262 __237__ 619

No___ 41 ___103 __237 __381

Total 161 365 574 1000

χ² = (Observed - Expected)²/Expected

Expected Values:

99.659 __ 225.935 __ 293.406

61.341 ___ 139.065 __ 180.594

The Chisquare values :

4.15172__ 5.7569__ 10.8438

6.74518_ 9.35307 __ 17.6176

χ² = 4.15172 + 5.7569 + 10.8438 + 6.74518 + 9.35307 + 17.6176 = 54.46827

Degree of freedom = (row-1)*(column-1) = (2-1)*(3-1) = 1*2 = 2

Pvalue at df = 2 ; Pvalue = 0

α = 0.05

Pvalue < Α ; Hence, we reject H0 ; and conclude that service subscription and age are not independent