Posted: September 16th, 2017
APUS Math302 quiz 4
Question 1 of 17
1.0 Points
Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.
Patient
1
2
3
4
5
6
7
Before
158
189
202
353
416
426
441
After
284
214
101
227
290
176
290
At the .01 level of significance, is there sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?
A.No
B.Yes
C.Cannot Determine
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Question 2 of 17
1.0 Points
Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.
Patient
1
2
3
4
5
6
7
Before
158
189
202
353
416
426
441
After
284
214
101
227
290
176
290
Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?
A.p = 2.7234
B.t = 2.7234
C.z = 1.8424
D.t = 1.8424
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Question 3 of 17
1.0 Points
Members of the general adult population volunteer an average of 4.2 hours per week. A random sample of 20 female college students and 18 male college students produced the results given in the table below. At the .01 level of significance, is there sufficient evidence to conclude that a difference exists between the mean number of volunteer hours per week for male and female college students?
Females
Males
Sample size
20
18
Sample mean
3.8
2.5
Sample variance
3.5
2.2
A.No, because the test value 2.38 is greater than the critical value
B.No, because the test value 2.38 does not exceed the critical value
C.No, because the test value 2.90 is greater than the critical value
D.Yes, because the test value 2.90 is greater than the critical value
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Part 2 of 8 –
Question 4 of 17
1.0 Points
If an estimated regression line has a Y-intercept of –7.5 and a slope of 2.5, then when X = 3, the actual value of Y is:
A.0
B.10
C.5
D.unknown
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Question 5 of 17
1.0 Points
The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. .
Store
1
2
3
4
5
6
Shelf Space
5
5
5
10
10
10
Weekly Sales
1.6
2.2
1.4
1.9
2.4
2.6
Store
7
8
9
10
11
12
Shelf Space
15
15
15
20
20
20
Weekly Sales
2.3
2.7
2.8
2.6
2.9
3.1
Is the correlation between weekly sales and shelf space significant at the .01 level of significance?
A.No, the sample correlation coefficient does not exceed the critical value.
B.
Yes, the computed t-test statistic is less than the critical value.
C.Yes, the p-value of the test for significance is less than .01.
D.Yes, the value of the test statistic does not exceed the critical value.
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Question 6 of 17
1.0 Points
In a simple linear regression analysis, the following sum of squares are produced:
f$sum{(y-ar{y})^{2}}f$ = 500
f$sum{(y-y’)^{2}}f$ = 100
f$sum{(y’-ar{y})^{2}}f$ = 400
The proportion of the variation in Y that is explained by the variation in X is:
A.80%
B.50%
C.20%
D.25%
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Question 7 of 17
1.0 Points
The regression line y’ = -3 + 2.5 X has been fitted to the data points (28, 60), (20, 50), (10, 18), and (25, 55). The sum of the squared residuals will be:
A.49.00
B.20.25
C.16.00
D.94.25
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Question 8 of 17
1.0 Points
Correlation is a summary measure that indicates:
A.the magnitude of difference between two variables
B.a curved relationship among the variables
C.the strength of the linear relationship between pairs of variables
D.the rate of change in Y for a one unit change in X
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Part 3 of 8 –
Question 9 of 17
2.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the 0.10 level of significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?
Pine trees
Spruce trees
Sample size
30
35
Mean trunk diameter (cm)
45
39
Sample variance
120
140
What is the test value for this hypothesis test?
Test value: Round your answer to three decimal places.
What is the critical value?
Critical value: Round your answer to three decimal places.
Part 4 of 8 –
Question 10 of 17
1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results:
Store Shelf Space(X) Weekly Sales(Y)
1 10 2.0
2 10 2.6
3 10 1.8
4 15 2.3
5 15 2.8
6 15 3.0
7 20 2.7
8 20 3.1
9 20 3.2
10 25 3.0
11 25 3.3
12 25 3.5
Find the equation of the regression line for these data. What is the value of the coefficient of determination? Place your answer, rounded to 3 decimal places, in the blank. Do not use a dollar sign. For example, 0.345 would be a legitimate entry.
Question 11 of 17
1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file ILE_and_DLH.xlsx
Treating ILE as the response variable, use regression to fit a straight line to all 18 data points.
Using your estimated regression output, predict the indirect labor expenses for a month in which the company has 31 direct labor hours.
Place your answer, rounded to 1 decimal place, in the blank. Do not use any stray punctuation marks or a dollar sign. For example, 458.9 would be a legitimate entry.
Part 5 of 8 –
Question 12 of 17
1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if the amount of money spent by its female charge customers differs, on average, from the amount spent by its male charge customers. To answer this question, an analyst collected random samples of 25 female customers and 22 male customers.
Based on these samples, on average, the 25 women charge customers spent $102.23 and the 22 men charge customers spent $86.46. Moreover, the sample standard deviation of the amount charged by the 25 women was $93.393, and the sample standard deviation of the amount charged by the 22 men was $59.695.
Suppose, using a 10% level of significance, you wish to know if there is sufficient evidence for Q-Mart to conclude that, on average, the amount spent by women charge customers differs from the amount spent by men charge customers. That is suppose you wish to test
H0: f$mu _{W} = mu _{M}f$ versus H1: f$mu _{W} eq mu _{M}f$
Assuming that the amounts spent by male and female charge customers at Q-Mart are normally distributed, based on the procedure advocated by Bluman, what is the test value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry.
Question 13 of 17
1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Are America’s top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO’s annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:
percent change for corporation 15 12 3 12 28 6 8 2
percent change for CEO 6 17 -4 12 32 -1 7 2
Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the p-value associated with this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.134 would be a legitimate entry.
Part 6 of 8 –
Question 14 of 17
3.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Researchers conducted an experiment to measure the effect of a drug on improving the quality of sleep as determined by how many more minutes of REM sleep were measured for each participant. One group of participants were given the experimental drug; the other (control) group was given a placebo. Does the evidence indicate that the drug improved the amount of REM sleep at a 0.01 level of significance? Answer each of the following parts.
Experimental group Control group
sample size 35 50
mean sleep improvement 12.8 9.1
sample variance 56.3 61.2
What is the test value for this hypothesis test?
Answer: Round your answer to two decimal places.
What is the P-value for this hypothesis test?
Answer: Round your answer to three decimal places.
What is the conclusion of this hypothesis test? Choose one.
1. There is sufficient evidence to show that the experimental drug improved the quality of sleep.
2. There is not sufficient evidence to show that the experimental drug improved the quality of sleep.
3. There is sufficient evidence to show that the quality of sleep is different for the experimental drug than for the control drug.
4. There is not sufficient evidence to show that the control drug decreased the quality of sleep.
Answer: Enter only a 1, 2, 3 or 4 for your answer.
Part 7 of 8 –
Question 15 of 17
1.0 Points
When testing the equality of two population variances, the test statistic is the ratio of the population variances; namely f$frac{sigma _{1}^{2}}{sigma _{2}^2}f$ .
True
False
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Part 8 of 8 –
Question 16 of 17
1.0 Points
If there is no linear relationship between two variables X and Y, the coefficient of determination, R2, must be f$pm f$ 1.0.
True
False
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Question 17 of 17
1.0 Points
In simple linear regression analysis, the relationship between the response variable Y and the explanatory variable X is a straight line. This means that all data points lie on the line.
True
False
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