Question

6) There are two car dealers in town. The mean monthly sales at Smith Auto and Jones Cars are about the same. However, Kevin Smith, owner of Smith Auto, believes his sales are more consistent. a) State the Hypothesis to show the variation in the monthly sales is lower at Smith Auto than Jones Cars. b) Choose a level of a Use a = 0.05 for this problem. c) To test the hypothesis, you collect monthly sales data for the two companies. The data appears in the Car Sales worksheet in the HW3 data on Moodle. Collect data and calculate necessary statistics to test the hypothesis. d) Sketch the sampling distribution. Include the critical value and test statistic. e) Draw a conclusion for the hypothesis test. Make sure you state your conclusion is in the context of the problem. f) Use Excel to perform the hypothesis test.

Smith Auto	Jones Cars
98	75
78	81
54	81
57	30
68	82
64	46
70	58
	101

Answer 1

Here we have data:

Smith Auto	Jones Cars
98	75
78	81
54	81
57	30
68	82
64	46
70	58
	101

Excel output:

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	69.85714286	69.25
Variance	218.8095238	526.7857143
Observations	7	8
Hypothesized Mean Difference	<
df	12
t Stat	0.061612134
P(T<=t) one-tail	0.475943007
t Critical one-tail	1.782287556
P(T<=t) two-tail	0.951886013
t Critical two-tail	2.17881283

Hypothesis:

H_o: μ₁ = μ₂

H_a: μ₁< μ₂

_{Test statistics:}

_{t = 0.06}

_{Critical value:}

_{t-critical = - 1.782}

_{P-value = p(t>|0.06|) = 0.4759}

Here we have not sufficient evidence to reject the null hypothesis, because t-observed value (0.06) is grater than t-critical value (-1.782) and not in rejection region.

Conclusion: Fail to reject the null hypothesis, we can say that, The mean monthly sales at Smith Auto and Jones Cars are about the same.