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Quantitative analysis

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Problem 1
The amount of fluid in a half-liter bottle of diet cola is normally distributed, and from past experience, the standard deviation is known to be 1.20 milliliters. A sample of 50 bottles reveals a mean weight of 502.1 ml. Construct and interpret a 90% confidence interval for the mean. Be sure to interpret the meaning of this interval.

Problem 2
A marketing firm recently studied the number of times men and women who live alone buy take-out dinners in a month. Two independent samples were taken, one with 35 men and another with 40 women. The mean number of take-out dinners for men is 24.51 with a known population standard deviation of 4.48, and the mean number of take-outs for women is 22.69 with a known population standard deviation of 3.86. Conduct a two-tailed hypothesis test to determine if the two means are different, with a .10 level of significance.

Problem 3: Conduct a one-tailed hypothesis test given the following information.
A test was conducted to determine whether gender of a spokesperson affected the likelihood that consumers would prefer a new product. A survey of consumers at a trade show employing a female spokesperson determined that 70 out of the 150 customers preferred the product, while 62 out of 180 customers preferred the product when a male spokesperson was employed. At the .01 level of significance, do the samples provide sufficient evidence to indicate that on the average, more consumers prefer a new product when the spokesperson is female?

Problem 4: Conduct a two-tailed hypothesis test given the following information.
The director of human resources at a large firm is comparing the distance traveled to work by employees in their office in downtown Atlanta with the distance for those in the downtown Jacksonville office. A sample of 17 Atlanta employees showed they travel a mean of 369 miles per month, with a sample standard deviation of 29 miles. A sample of 14 Jacksonville employees showed they travel a mean of 381 miles per month, with a sample standard deviation of 25 miles. At the .01 level of significance, is there a difference in the mean number of miles traveled between the two groups?

Problem 5: Define autocorrelation in the following terms
a. In which type of regression is it likely to occur?
b. What is the negative impact of autocorrelation in a regression?
c. Which method is used to determine if it exists?
d. If found in a regression, how is autocorrelation eliminated?

Problem 6: Define multicollinearity in the following terms
a. In which type of regression is it likely to occur?
b. What is the negative impact of multicollinearity in a regression?
c. Which method is used to determine if it exists?
d. If multicollinearity is found in a regression, how is it eliminated?

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Solution Summary

The solution provides step by step method for the calculation of different statistical techniques . Formula for the calculation and Interpretations of the results are also included.

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BIOSTATISTICS

2.A group of 25 subjects have their diastolic blood pressures measured. The results, in SPSS are:

|-----------|-------|--------|
|N |Valid |25 |
|-------|--------|
| |Missing|0 |
|-----------|-------|--------|
|Median |85.00 |
|-------------------|--------|
|Mode |82.00 |
|-------------------|--------|
|Minimum |55.00 |
|-------------------|--------|
|Maximum |110.00 |
|-----------|-------|--------|
|Percentiles|25 |71.00 |
| |-------|--------|
| |50 |85.00 |
| |-------|--------|
| |75 |98.00 |
|--------|-------|--------|

Don't worry about values exactly at the endpoints of these intervals. Do the calculations roughly.
(1 point each)

a. What percentage of subjects were from 55 to 85?
b. What percentage of subjects were < 85?
c. What percentage of subjects were from 71 to 85?
d. What percentage of subjects were > 71?
e. What percentage of subjects were > 98?
f. Is there one value more common than the rest, and if so, what is it?

3. Assume you have already been give a Z value. This saves you a step. Consider and determine the following probabilities (1 point each).

A. Pr (-1 < Z < 1)
B. Pr (0 < Z < 1)
C. Pr (Z > 1)
D. Pr (-1 < Z < 0)
E. Pr (Z < -1)
F. Pr (Z > -2)
G. Pr (-1 < Z < 2)

4. Suppose the mean systolic blood pressure in a group of individuals is 150 mmHg, with a standard deviation of 15. Assuming SBP follows a normal distribution in this population, compute (1 point each):

A. Pr (135 < value < 165)
B. Pr (value > 165)
C. Pr (value < 135)
D. Pr (138.75 < value < 161.25)

5 Compute the 5th, 50th, and 95th percentiles of SBP from the previous question. (3 points: 1 each).

In questions 6 - 8, use the 1 and 2 SD rules, without the table.

6.In general, what percentage of a Gaussian data set is within 1 SD of the mean? What percentage is within 2 SD's of the mean? (2 points: 1 each)

7.If the mean grade on an exam was 80, SD = 6, where did about 68% of the grades fall? How about 95%? Assume the grades are Gaussian. (2 points).

8.Consider the following data: 1, 1, 2, 2, 4, 5, 6, 9, 40, 200

Use the 68% and 95% rules to test the normality of these data. (2 points).

9.A researcher studying a subtype of lymphocytes obtains a sample mean of 100 per mL, and a standard deviation of 20, with 25 subjects. Within what interval can you be roughly 68% sure the population mean number of these cells per mL lies? How about 95% sure? (2 points)

10.A researcher has a sample of 500 subjects. The mean is 40, median is 20, range 10-100. (2 points each)

a.Could this researcher calculate a useful interval with 95% probability of containing the population mean (using the mean and SEM)? Explain

b.Could the researcher use the mean and SD to usefully estimate where 95% of the individual subject values were? Explain

c)If there were 10 subjects, would your answers to a and b change?

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