T-test Questions

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.