Question

A researcher at the Nie Pójdzie Motor Club is interested in the average repair bill for automobile owners when the “check engine” light comes on. He believes that automobiles manufactured overseas (Import) will have lower repair costs (in dollars) than automobiles manufactured in the United States (Domestic). A random sample from each type of manufacturer was drawn. The Data Analysis output for the various tests used when comparing two group means are shown below. The significance level was .05. Identify which two sample test should be performed from the scenario and from the following outputs.

F-Test Two-Sample for Variances
	Import	Domestic
Mean	331.2	349.6
Variance	569.07	104.27
Observations	10	10
df	9	9
F	5.4578
P(F<=f) one-tail	0.0094
F Critical one-tail	3.1789

t-Test: Two-Sample Assuming Equal Variances
	Import	Domestic
Mean	331.2	349.6
Variance	569.07	104.27
Observations	10	10
Pooled Variance	336.67
Hypothesized Mean Difference	0
df	18
t Stat	-2.2423
P(T<=t) one-tail	0.0189
t Critical one-tail	1.7341
P(T<=t) two-tail	0.0378
t Critical two-tail	2.1009

t-Test: Two-Sample Assuming Unequal Variances
	Import	Domestic
Mean	331.2	349.6
Variance	569.07	104.27
Observations	10	10
Hypothesized Mean Difference	0
df	12
t Stat	-2.242
P(T<=t) one-tail	0.0223
t Critical one-tail	1.7823
P(T<=t) two-tail	0.0446
t Critical two-tail	2.1788

t-Test: Paired Two Sample for Means
	Import	Domestic
Mean	331.2	349.6
Variance	569.07	104.27
Observations	10	10
Pearson Correlation	1.00
Hypothesized Mean Difference	0
df	9
t Stat	-4.263
P(T<=t) one-tail	0.0011
t Critical one-tail	1.8331
P(T<=t) two-tail	0.0021
t Critical two-tail	2.2622

a) What is the appropriate two sample test to perform – the paired t test, the t test assuming equal variances, or the t test assuming unequal variances – for this research project?

b) State the H₀ and H_a.

c) Identify the decision rule using the critical value of t (round to three decimal places).

d) Identify the decision rule using the p value method.

e) State the test statistic (t _calc).

f) Do you reject or not reject Ho? Explain your decision.

Answer 1