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

	1	2	3	4
	20.8	16.3	16.8	16.7
	20.4	14.5	20.9	14.5
	25.1	10.4	28.4	13.7
	27.4	12.2	22.5	15.4
	15.4	12.5	17.5	12.4
	15.3	9.5	14.9	16
	13.9	15.3	22.4	7.5
			17.5	12.9
			25.4	18.3
			22.4
Mean	19.75714	12.95714	20.87	14.15556
SD	5.190009	2.527091	4.209526	3.120141
n	7	7	10	9

Mean = AVEARGE()

SD = STDEV()

10)

mean mileage of make 2

Margin of error = tc*(S/SQRT(n)) = 2.3372

95% CI of mean mileage of make 2

CI
tc	2.446912	T.INV.2T(α,df)
Upper	15.29428	X bar + tc*(S/SQRT(n))
Lower	10.61992	X bar - tc*(S/SQRT(n))

11) Lower CI limit = 10.6199

12) Upper CI limit = 15.2943

13)

Hypothesis:

Ho: μ1​ = μ2​

Ha: μ1​ ≠ μ2​

Test:

Sp^2

13.18642791

((n1-1)S1^2+(n2-1)S2^2)/(n1+n2-2)

t stat

-4.421775145

(X1 bar-X2 bar )/SQRT(Sp*(1/n1 + 1/n2))

P value

0.000494862

T.DIST.2T(ts,df)

P value < 0.05, reject H0

There is enough evidence to claim mean mileage of makes 2 and 3 are differ