Question

Test the claim that the mean gas MPG (city) is equal for all three car sizes. This requires the use of one-way ANOVA (single factor) to test for equality of three or more means (12.2). Calculate the null and alternate hypothesis, test statistic, critical value, p-value, and state the conclusion.

Size Class	Gas MPG - City Driving
Small	25
Small	27
Small	25
Small	25
Small	29
Midsize	19
Small	22
Midsize	20
Midsize	21
Midsize	21
Small	20
Midsize	23
Midsize	19
Large	18
Large	18
Midsize	19
Large	19
Large	15
Large	17
Large	16
Large	16

	Small	Midsize	Large
City MPG

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂ = u₃

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 23.95

F_critical = 3.55

The P-value = less than 0.001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

Conclusion:-

Reject H₀, There is sufficient evidence for significant differences between the three cars sizes.