Question

A consulting company was tasked with identifying which market segment would be more profitable, labeled as Segment A or Segment B. A survey was created showing a product to the two different segments, and respondents were asked to rate the product on a scale from 1 to 10 (1 worst, 10 best). Run the correct test using α=0.10 . Which is the correct conclusion?

		There is no statistically significant difference between Segments A and B.
		Cannot run this test, data not normal or not enough sample size.
		There is a statistically significant difference between Segments A and B.

Segment	Product Rating
A	6
A	5
A	2
A	2
A	10
A	9
A	9
A	8
A	6
A	9
A	6
A	5
A	8
A	10
A	4
A	9
A	4
A	2
A	4
A	5
A	8
A	6
A	7
A	7
A	4
A	7
A	7
A	6
A	7
A	10
B	8
B	1
B	3
B	7
B	6
B	5
B	4
B	1
B	7
B	2
B	1
B	7
B	9
B	2
B	1
B	4
B	7
B	1
B	9
B	9
B	8
B	4
B	10
B	5
B	10
B	10
B	10
B	3
B	1
B	2

Answer 1

For Segment A, sample 1 :

Sample mean, x̅1 = 6.4

Sample standard deviation, s1= 2.372253

For Segment A,ample size, n1 = 30

For Segment B, sample 2 :

Sample mean, x̅2 = 5.233333

Sample standard deviation, s2 = 3.297683

Sample size, n2 = 30

α = 0.1

Null and Alternative hypothesis:

Ho : µ1 = µ2     

H1 : µ1 ≠ µ2     

Pooled variance :     

S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2) = 8.251149    

Test statistic:     

t = (x̅1 - x̅2)/[√(s²p(1/n1 + 1/n2 )] = 1.5730    

df = n1+n2-2 = 58    

Critical value :     

Two tailed critical value, t crit = T.INV.2T(0.1, 58 ) = ± 1.672

p-value :     

Two tailed p-value =T.DIST.2T(ABS(1.5730), 58) = 0.1212

Decision:     

p-value > α, Do not reject the null hypothesis     

Answer: There is no statistically significant difference between Segments A and B.