Question

A survey was conducted to compare the mean cost of a meal at fast food restaurants in two different cities.

City n x s
A 26 $4.05 $0.55
B 32 $5.15 $0.85

Assume that the population variances of both groups are different. Test if there is sufficient evidence that the mean costs of a meal at fast food restaurants in two different cities are different. Conduct the hypothesis testing (optional) in paper.

Answer 1

We reject the Null and conclude that the mean costs of a meal at fast food restaurants in two different cities are different.

Explanation:

Given :

City n x s

A 26 $4.05 $0.55

B 32 $5.15 $0.85

H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 ≠ 0

n1 = 26 ; x1 = 4.05 ; s1 = 0.55

n2 = 32 ; x2 = 5.15 ; s2 = 0.85

Tstatistic :

(x1 - x2) / √(s1²/n1 + s2²/n2)

(4.05 - 5.15) / √(0.55²/26 + 0.85²/32)

-1.1 / 0.1849668

= - 5.947

Using the smaller n;

df = n - 1 ; 26 - 1 = 25

Pvalue = (-5.947, 24)

Pvalue = 0.000001

Since Pvalue < α ; We reject the Null and conclude that the mean costs of a meal at fast food restaurants in two different cities are different.