Question

Random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below.

Model A / Model B / Model C / Model D
   29  /   29   /   29   /   26
   27  /   26   /   24   /   21
   24  /   21   /   27   /   24
   23  /   21   /   22   /   29

Test the claim that the four different models have the same population mean. Use a significance level of 0.05. Show all work please

Answer 1

A	B	C	D
29	27	24	23
29	26	21	21
29	24	27	22
26	21	24	29

Using Excel, go to Data, select Data Analysis, choose Anova: Single Factor and group by columns.

SUMMARY
Groups	Count	Sum	Average	Variance
A	4	113	28.25	2.25
B	4	98	24.50	7.00
C	4	96	24.00	6.00
D	4	95	23.75	12.92
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	53.25	3	17.75	2.52	0.11	3.49
Within Groups	84.5	12	7.04
Total	137.75	15

H0: μ1 = μ2 = μ3 = μ4

H1: At least one μi is different from others

p-value = 0.11

Since p-value is more than 0.05, we do not reject the null hypothesis and conclude that μ1 = μ2 = μ3 = μ4.

So, the four different models have the same population mean.