math 8
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ShortExercise8.docxBUSA 2183 Introduction to Business Statistics
Summer 2019 –Session II
IMPORTANT: In any question, if there is a calculation, first provide the formula and then show your calculations for your answers.
Please, provide your answers under each question.
Data files can be found in the D2L.
Question 1 (Short Exercise 6 in the book) (3*2=6 points)
A population consists of the following five values: 2, 2, 4, 4, and 8.
a. List all samples of size 2, and compute the mean of each sample.
b. Compute the mean of the distribution of sample means and the population mean. Compare the two values.
c. Compare the dispersion in the population with that of the sample means.
Question 2 (Short Exercise 16 in the book) (3*2=6 points)
A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Compute the probability the sample mean is:
a. Less than 74.
b. Between 74 and 76.
c. Greater than 77.
Question 3 (Short Exercise 32 in the book) (4*2=8 points)
Majesty Video Production Inc. wants the mean length of its advertisements to be 30 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 16 ads produced by Majesty.
a.What can we say about the shape of the distribution of the sample mean time?
b.What is the standard error of the mean time?
c.What percent of the sample means will be greater than 31.25 seconds?
d.What percent of the sample means will be greater than 28.25 but less than 31.25 seconds?
Question 4 (Short Exercise 11 in the book) (2.5*2=5 points)
Appendix B.4 is a table of random numbers that are uniformly distributed. Hence, each digit from 0 to 9 has the same likelihood of occurrence.
You can find the data file in D2L.
|
0 |
2 |
7 |
1 |
1 |
|
9 |
4 |
8 |
7 |
3 |
|
5 |
4 |
9 |
2 |
1 |
|
7 |
7 |
6 |
4 |
0 |
|
6 |
1 |
5 |
4 |
5 |
|
1 |
7 |
1 |
4 |
7 |
|
1 |
3 |
7 |
4 |
8 |
|
8 |
7 |
4 |
5 |
5 |
|
0 |
8 |
9 |
9 |
9 |
|
7 |
8 |
8 |
0 |
4 |
a.Draw a graph showing the population distribution of random numbers. What is the population mean?
b.Following are the first 10 rows of five digits from the table of random numbers in Appendix B.4 . Assume that these are 10 random samples of five values each. Determine the mean of each sample and plot the means on a chart similar to Chart 8–4 . Compare the mean of the sampling distribution of the sample mean with the population mean.
