Download HOMEWORK 5A--GENDER AND STATISTICS GRADES-

SAMPLE PROBLEM--MEAN MILES-PER-GALLON OF TWO AUTOMOBILES
1. Use spreadsheet << T12MEANS >> to conduct estimation and hypothesis testing on
the population mean miles-per-gallon of two different automobiles. Each car was
fitted with an automatic miles-per-gallon computing device, and was driven by the
same driver over the same 40-mile route.
Car X
Car Y
27.3, 25.5, 29.6, 32.3, 25.9, 24.1, 22.9, 24.6, 23.2, 20.0, 24.3
28.6, 26.3, 25.3, 24.8, 25.9, 22.5, 32.4, 24.6, 24.3
a. The sample size is:
Car X:
11
Car Y:
9
b. The sample mean is:
Car X:
25.4273
Car Y:
26.0778
c. The estimated population standard deviation is:
Car X:
3.36009
Car Y:
2.88954
d. The point estimate of the population mean is:
Car X:
25.4273
Car Y:
26.0778
e. The sampling standard deviation (standard error) of the sample means is:
Car X:
1.01310
Car Y:
0.963180
f.
The 95% confidence interval for the population mean is:
(use point estimate ± error factor format, not LCL and UCL)
Car X: μx = 25.42733 ± 2.25734 Car Y: μy = 26.0778 ± 2.22110
Test the H0 that each population mean is 27.00 m.p.g. against the Ha
that it is not 27.00.
g. State the H0:
Car X:
μx = 27.00
Car Y:
μy = 27.00
h. State the Ha:
Car X:
μx ≠ 27.00
Car Y:
μy ≠ 27.00
i.
Use α = 0.05. State the tt, table-t, or critical value:
Car X:
tt = ± 2.228
Car Y:
tt = ± 2.306
j.
The tc, calculated-t or test statistic is:
Car X:
tc = - 1.55238
Car Y:
tc = - 0.957476
k. The hypothesis-test conclusion is:
Car X: H0 is not rejected.* Car Y:
H0 is not rejected.**
* The difference between the sample mean, 25.43, and the null hypothesis, 27.00, is not
statistically significant at the 0.05 level. The population mean could be 27.00.
** The difference between the sample mean, 26.08, and the null hypothesis, 27.00, is not
statistically significant at the 0.05 level. The population mean could be 27.00.
l. What is the p-value in this test?
Car X: 0.151619
Car Y:
0.366364
2. Using the same data, conduct estimation and hypothesis testing on the
difference between population mean miles-per-gallon of car X and car Y.
a.The point estimate of the difference between population means is:
- 0.650505
b. The sampling standard deviation (standard error) of the differences between
sample means is:
1.42014
c. The 95% confidence interval for the difference between population means is
(use point estimate ± error factor format, not LCL and UCL)
(μ1 - μ2) = - 0.650505 ± 2.98361
Test the H0 that the population means are equal against the Ha that they are not
equal.
d. State the H0:
(μ1 - μ2) = 0
e. State the Ha:
(μ1 - μ2) ≠ 0
f. Use α = 0.05. State the tt, table-t, or critical value:
g. The tc, calculated-t or test statistic is:
± 2.10092
- 0.458056
h. The hypothesis-test conclusion is: H0 is not rejected. *
* The difference between the sample means, 0.6505, is not statistically significant at the 0.05 level.
The population means could be equal.
i. What is the p-value in this test?
0.652394