Question

1	20.8
1	20.4
1	25.1
1	27.4
1	15.4
1	15.3
1	13.9
2	16.3
2	14.5
2	10.4
2	12.2
2	12.5
2	9.5
2	15.3
3	16.8
3	20.9
3	28.4
3	22.5
3	17.5
3	14.9
3	22.4
3	17.5
3	25.4
3	22.4
4	16.7
4	14.5
4	13.7
4	15.4
4	12.4
4	16
4	7.5
4	12.9
4	18.3

nCalculate a 95% confidence interval for the mean mileage of make 2. Use the method for single meanswhen σ is not known, but use the Error Mean Square as the estimate of the variance. The degrees of freedom will be the Error DF, not n‑1!

Reminders:

Confidence Interval = mean ± margin of error

Margin of error = critical value * standard error

Use critical value for T at a/2 = 0.025 and df = error df  (t table or EXCEL T.INV function)

Use standard error = Ö(error mean square/number of observations of that make of car)

10. What was the margin of error for the confidence interval for gasoline mileage of make 2?

11. What was the lower 95% confidence limit for make 2 mileage?

12. What was the upper 95% confidence limit for make 2 mileage?

                                                                                                                                      {Example 24}

nConduct a test of hypothesis that the mean mileage of makes 2 and 3 do not differ. Use the method for single means when σ is not knownwith the Error MS serving as the pooled variance.

Reminders:

            Test statistic t = difference of means / standard error of difference of means.

The standard error of the difference equals square root of the sumof variances of the two means. The variance of each mean is estimated by the error mean square/number of observations in that mean.

13. What is the value of the t test statistic for testing the hypothesis that makes 2 and 3 do not differ in mileage?

Answer 1

Result:

Result:

MINITAB used.

One-way ANOVA: mileage versus make

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
make	4	1, 2, 3, 4

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
make	3	389.7	129.90	8.61	0.000
Error	29	437.3	15.08
Total	32	827.0

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
3.88320	47.12%	41.65%	31.37%

Means

make	N	Mean	StDev	95% CI
1	7	19.76	5.19	(16.76, 22.76)
2	7	12.957	2.527	(9.955, 15.959)
3	10	20.87	4.21	(18.36, 23.38)
4	9	14.16	3.12	(11.51, 16.80)

Pooled StDev = 3.88320

95% CI for make 2 = (9.955, 15.959)