STATS Practice Problems Assignment 2015

STATS Practice Problems Assignment 2015

Question 1 of 17

A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men. Assume? = 0.05. What is the test value?

Women Men
Sample size 50 80
Mean effect 7 6.95
Sample variance 3 4
A.t = 3.252
B.t = 0.151
C.z = 0.081
D.z = 0.455
Question 2 of 17

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

What is the p-value associated with the test of hypothesis you conducted?

A.p = .057493
B.p = .114986
C.p = .942597
D.p = .885014
Question 3 of 17

A fiA 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 .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 40 70
Mean trunk diameter (cm) 45 39
Sample variance 100 150
A. The data do not support the claim because the test value 1.29 is greater than 1.28.
B.The data do not support the claim because the test value 1.29 is less than 1.64.
C. The data support the claim because the test value 2.78 is greater than 1.64.
D.The data support the claim because the test value 2.78 is greater than 1.28.
Part 2 of 8 –
Question 4 of 17

In choosing the “best-fitting” line through a set of points in linear regression, we choose the one with the:

A.largest number of points on the line
B.largest sum of squared residuals
C.smallest sum of squared residuals
D.smallest number of outliers
Question 5 of 17

The correlation value ranges from

A.–2 to +2
B.0 to +1
C.–1 to +1
D.-3 to +3
Question 6 of 17

An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost of apartments based on the size of the apartment. Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx. ( The excel document is attached)

At the .05 level of significance determine if the correlation between rental cost and apartment size is significant.

A.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the p-value for this test is less than .0001.
B.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient 0.85 exceeds 0.50.
C.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the t-test value, 7.74, is greater than the critical value 1.96.
D.No, there is not a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient is less than .95.
Question 7 of 17

A linear regression analysis produces the equation

y = 5.32 + (-0.846)x

Which of the following statements must be true?

A.As x increases, y decreases, and the correlation coefficient must be positive.
B.As x increases, y decreases, and the correlation coefficient must be negative.
C.As x increases, y increases, and the correlation coefficient must be positive.
D.As x increases, y increases, and the correlation coefficient must be negative.
Question 8 of 17

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

What is the estimated regression equation?

A. y^= 1.45 + 0.724x
B. y^= 2.63 – 0.174x
C.y^ = 1.45 + 0.074x
D. y^= 2.63 + 0.724x
Part 3 of 8 –
Question 9 of 17

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 20 30
Mean trunk diameter (cm) 45 39
Sample variance 100 150

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

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 Excel Document is attached

Treating ILE as the response variable, use regression to fit a straight line to all 18 data points. What values for the intercept (a) and slope (b) do you obtain?

Place your answers, rounded to 3 decimal places, in the blanks provided. Do not use any stray punctuation marks. For example, 34.567 would be a legitimate entry.

intercept (a) =
slope(b) =

Question 11 of 17

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

Using the equation of the regression line for these data, predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.
Place your answer, rounded to 3 decimal places , in the blank. Do not use a dollar sign. For example, 2.345 would be a legitimate entry.

Part 5 of 8 –
Question 12 of 17

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:?W= ?M

versus H1:?W ?M

Assuming that the amounts spent by female and male charge customers at Q-Mart are normally distributed, based on the procedure advocated by Bluman, what is/are the critical values that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. If there are two critical values, place only the positive value in the blank. For example, 2.035 would be a legitimate entry.

Question 13 of 17

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.

Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 8 unacceptable assemblies.

If you are interested in determining if there is sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies, what is the p-value associated with such a test of hypothesis?

Place your answer, rounded to 4 decimal places, in the blank. For example, .0123 would be a legitimate entry.

Part 6 of 8 –
Question 14 of 17

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

In conducting hypothesis testing for difference between two means when samples are dependent (paired samples), the variable under consideration is

__

D ; the sample mean difference between the pairs.

True
False
Part 8 of 8 –