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Homework answers / question archive / 1) A real estate agent gathered data from homes that recently sold in two local neighborhoods
1) A real estate agent gathered data from homes that recently sold in two local neighborhoods. It was decided to test to determine the relationship of the mean land values from the two neighborhoods. The following printout was generated using the individual sample variances as estimates of the unknown population variances.
HYPOTHESIS: MEAN X = MEAN Y
land_value BROKEN DOWN BY neighborhood
X = land value(neighborhood=0)
Y = land value(neighborhood=1)
SAMPLE MEAN OF X = 14974.5
SAMPLE VARIANCE OF X = 9.91609E6
SAMPLE SIZE OF X = 25
SAMPLE MEAN OF Y = 49443
SAMPLE VARIANCE OF Y = 2.73643E8
SAMPLE SIZE OF Y = 25
MEAN X - MEAN Y = -34468.5
t = -10.2346
D. F. = 48
P-VALUE = 2.00396E-10
P-VALUE/2 = 1.00198E-10
SD. ERROR = 3367.84
State the desired alternative hypothesis to be conducted to determine if neighborhood 1 had a higher mean land value than did neighborhood 0.
1) Ha: mu0 - mu1 < 0
2) Ha: mu0 - mu1 > 34,468.5
3) Ha: mu0 - mu1 > 0
4) Ha: mu0 - mu1 = 0
2) Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package.
HYPOTHESIS: MEAN X = MEAN Y
SAMPLES SELECTED FROM SALARY
X = Consumer Products
Y = Telecommunications
SAMPLE MEAN OF X = 1761
SAMPLE VARIANCE OF X = 3.97555E6
SAMPLE SIZE OF X = 21
SAMPLE MEAN OF Y = 1093.5
SAMPLE VARIANCE OF Y = 103255
SAMPLE SIZE OF Y = 21
MEAN X - MEAN Y = 667.5
test statistic = 1.47809
D. F. = 40
P-VALUE = 0.147626
P-VALUE/2 = 0.0738131
SD. ERROR = 451.597
Which of the following assumptions are necessary to perform the test above?
1) The pooled variance equals the average of the two sample means.
2) The population mean salaries are equal.
3) The samples were independently collected.
4) Both populations of salaries for the two industries have approximate normal distributions.
3. Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package.
HYPOTHESIS: MEAN X = MEAN Y
SAMPLES SELECTED FROM SALARY
X = Consumer Products
Y = Telecommunications
SAMPLE MEAN OF X = 1761
SAMPLE VARIANCE OF X = 3.97555E6
SAMPLE SIZE OF X = 21
SAMPLE MEAN OF Y = 1093.5
SAMPLE VARIANCE OF Y = 103255
SAMPLE SIZE OF Y = 21
MEAN X - MEAN Y = 667.5
test statistic = 1.47809
D. F. = 40
P-VALUE = 0.147626
P-VALUE/2 = 0.0738131
SD. ERROR = 451.597
Using alpha = .05, give the rejection region for a two-tailed test.
1) Reject H0 if t > 1.684.
2) Reject H0 if t > 1.684 or t < -1.684.
3) Reject H0 if t > 2.021 or t < -2.021.
4) Reject H0 if t > 2.021.
1. A real estate agent gathered data from homes that recently sold in two local neighborhoods. It was decided to test to determine the relationship of the mean land values from the two neighborhoods. The following printout was generated using the individual sample variances as estimates of the unknown population variances.
State the desired alternative hypothesis to be conducted to determine if neighborhood 1 had a higher mean land value than did neighborhood 0.
The alternative hypothesis is that mu1 > mu0. This is the same as mu1 - mu0 > 0, which is the same as mu0 - mu1 < 0. The answer is (1).
2. Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package.
Which of the following assumptions are necessary to perform the test above?
The test is a two-sample t test. This test assumes that the two samples are independent and that the populations are both normal or the sample sizes are large. Since the sample sizes are relatively large, the assumption that needs to be met is that the samples are independent. The answer is (3).
3. Data were collected from CEO's in the consumer products and telecommunication industries. It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using the ASP software package.
Using alpha = .05, give the rejection region for a two-tailed test.
Since this is a two-tailed test, the answer either has to be (2) or (3). The degrees of freedom for a t-test are n1 + n2 - 2, so here, df = 21 + 21 - 2 = 40. The critical value for t at the alpha = .05 level is t = 2.021 (found by looking at a t-distribution table with 40 degrees of freedom). The answer is (3).
