Download HOMEWORK 5A--GENDER AND STATISTICS GRADES-

SAMPLE PROBLEM 5A--MEAN MILES-PER-GALLON OF TWO AUTOMOBILES
1. Use spreadsheet << Z12MEANS >> 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 each day for 50
consecutive days. On half of the days, car X was driven first, and on the other
half of the days, car Y was driven first.
Car X
Car Y
Sample
Size
60
50
Sample
Mean
28.44
27.50
Estimated Population
Standard Deviation
5.32
5.03
a. The point estimate of the population mean is:
Car X:
28.44
Car Y:
27.50
b. The sampling standard deviation (standard error) of the sample means is:
Car X:
0.686809
Car Y:
0.711349
c. The 95% confidence interval for the population mean is:
(use point estimate ± error factor format, not LCL and UCL)
Car X: μx = 28.44 ± 1.34612
Car Y: μy = 27.50 ± 1.39422
d. What sample size is needed for an error factor "E" of ± 1.0 m.p.g.?
Car X:
108
Car Y:
98
Test the H0 that each population mean is 27.00 m.p.g. against the Ha that it is
not 27.00.
e. State the H0:
Car X:
μx = 27.00
Car Y:
μy = 27.00
f. State the Ha:
Car X:
μx ≠ 27.00
Car Y:
μy ≠ 27.00
g. Use α = 0.05. State the zt, table-z, or critical value:
Car X:
zt = ± 1.960
Car Y:
zt = ± 1.960
h. The zc, calculated-z or test statistic is:
Car X:
zc = 2.09665
Car Y:
i. The hypothesis-test conclusion is:
Car X: H0 is rejected. *
Car Y:
zc = 0.702889
H0 is not rejected **
* The difference between the sample mean, 28.44, and the null hypothesis, 27.00, is
statistically significant at the 0.05 level. The population mean is probably not 27.00.
** The difference between the sample mean, 27.50, and the null hypothesis, 27.00, is not
statistically significant at the 0.05 level. The population mean could be 27.00.
j. What is the p-value in this test?
Car X: 0.0360243
Car Y:
0.482125
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:
0.94
b. The sampling standard deviation (standard error) of the differences between
sample means is:
0.988800
c. The 95% confidence interval for the difference between population means is
(use point estimate ± error factor format, not LCL and UCL)
(μ1 - μ2) = 0.94 ± 1.93801
d. What sample size is needed for an error factor "E" of ± 1.40 m.p.g.?
106
Test the H0 that the population means are equal against the Ha that they are
not equal.
e. State the H0:
(μ1 - μ2) = 0
f. State the Ha:
(μ1 - μ2) ≠ 0
g. Use α = 0.05. State the zt, table-z, or critical value:
h. The zc, calculated-z or test statistic is:
± 1.960
0.950648
i. The hypothesis-test conclusion is: H0 is not rejected. *
* The difference between the sample means, 0.94, is not statistically significant at the 0.05
level. The population means could be equal.
j. What is the p-value in this test?
0.341783