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Statistics Assignment
6. 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 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.
10. There are five sales associates at mid-motors ford. The five representatives and the number of cars they sold last week are:
Sales. Cars Sold
Representative.
Peter Staller. 8
Connie Stallter. 6
Juan Lopez. 4
Ted Barnes. 10
Peggy Chu 6
A. How many different samples of size 2 are possible?
B. List all possible samples of size 2, and compute the mean of each sample
C. Compare the mean of the sampling distribution of sample means with that of the population
D. On a chart compare the dispersion in sample means with that of the population.
12. Scrapper elevator company has 20 sales representatives who sell its product through out the US and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be population values.
2 3 2 3 3 4 2 4 3 2 2 7 3 4 5 3 3 3 3 5
A. Draw a graph showing the population distribution
B. compute the mean of the population
C. Select five random samples of 5 each. Compute the mean of each sample. Use the methods described the methods to be used in order to determine the items to be included in the sample.
D. Compare the mean of the sampling distribution of the sample means to the population mean. Would you expect the two values to be about the same?
E. draw a histogram of the sample means. Do you notice the difference in the shape of the distribution of sample means compared to the shape of the population distribution?
16. 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. Between 76 and 77
D. Greater than 77
18. According to an IRS study it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A customer watchdog agency selects a random sample of 40 tax payers.
A. What is the standard error of the mean in this example?
B. what is the likelihood that sample mean is greater than 320 minutes?
C. What is the likelihood the sample mean is between 320 and 350 minutes?
D. What is the likelihood the sample mean is greater than 350 minutes?
Please see the attachment for solution.
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xxxxxx see xxx xxxxxxxxxx xxx solution. xx xxx need xxx xxxxxxxxxxxxx please xxx me. xxxxxxx
xxxxxx The normal probability P(Z < z) can be calculated using the Excel formula
xxxxxxxxxxxxx xxx the xxxxx xxxx xxx computation]
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xx A xxxxxxxxxx consists xx the xxxxxxxxx xxxx xxxxxxx 2,2,4,4 and xxxxxxx List all samples of xxxx 2 xxx xxxxxxx the mean xx xxxx sample.�B. xxxxxxx xxx mean xx xxxxxxxxxxxx of xxxxxx xxxxx and the xxxxxxxxxx mean. Compare the two values.�C. xxxxxxx xxx dispersion xx xxx xxxxxxxxxx xxxx that of xxx xxxxxx xxxxxxx
xxxxxxxxx
xx
xxxxxxxxxxxxxxxxxxxxxSample | xxxxxx | Mean | |
x | 2 | x | 2 |
x | 2 | x | x |
x | x | 4 | x |
4 | 2 | x | x |
x | x | x | x |
6 | x | x | 3 |
x | x | x | x |
8 | x | x | 4 |
9 | 4 | x | 6 |
xx | 4 | x | 6 |
xx xxx population xxxxx
x xxx x x x x + x + xxxx x xxxx = x
xxx xxxx of xxxxxxxxxxxx xx sample means,
x (2 x x x x + x x x + x + x x 4 + 6 + xxxxx = xxxxx = xx
xxxxx xxx xxxx of distribution of sample xxxxx xxx the population mean are xxxxxxx
xx The xxxxxxxxxx for xxx population xx xxxxxxx
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xxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxSample | Values | xxxx | xxxxxx | xxxx sold | xxxx | xxxx sold | xx xx xxxxx | xx of xxxxx | ||
x | 2 | x | 2 | 1 | 8 | 6 | x | 4 | x | 0 |
x | x | 4 | x | x | x | x | 6 | 5 | x | x |
x | 2 | x | 3 | x | x | xx | x | x | x | 2 |
x | 2 | 8 | x | 4 | 8 | 6 | x | x | 0 | x |
x | x | x | 3 | x | 6 | x | 5 | 8 | 1 | 2 |
6 | 2 | x | 3 | x | 6 | 10 | 8 | x | 0 | 1 |
7 | 2 | x | x | 7 | x | 6 | 6 | xx | 1 | x |
x | x | 4 | 4 | x | x | xx | x | |||
9 | x | x | 6 | x | x | x | 5 | |||
10 | x | 8 | x | 10 | xx | x | x |
6,10
x12
xxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxData | Units sold | xxxxxxxxx | xxxxxx | xxxxxx Values | xxxx | ||||
2 | x | 0 | x | 3 | x | 2 | x | x | 2.8 |
3 | 2 | x | 2 | 2 | x | x | x | x | 3.2 |
2 | 3 | x | 3 | x | 4 | 3 | x | 5 | 3.4 |
3 | 4 | x | x | 4 | x | 7 | 3 | x | xxx |
x | x | 2 | x | 2 | x | x | 4 | 3 | xxx |
x | 6 | x | |||||||
2 | 7 | x | |||||||
4 | |||||||||
x | |||||||||
2 | |||||||||
x | Sample xxxx | Frequency | |||||||
x | 2.8 | x | |||||||
x | 3.2 | x | |||||||
4 | xxx | x | |||||||
x | 3.8 | 1 | |||||||
x | |||||||||
3 | |||||||||
x | |||||||||
x | |||||||||
x |
xxxxx
xxx0 |
5 |
9 |
x |
x |
0 |
1 |
x |
2 |
1 |
1 |
Question 16 | Question 18 | ||||
x | x | xxx < z) | x | x | P(Z < xx |
xx | -1.2649 | 0.1030 | xxx | -0.7906 | xxxxxx |
76 | xxxxxx | xxxxxx | 350 | xxxxxx | 0.9431 |
xx | 2.5298 | xxxxxx |
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xx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | |||||||||||
Population xxxx | x | x | 2 | , | x | x | 4 | , | x | ||
Required: | |||||||||||
A. List all samples of xxxx x and xxxxxxx the xxxx xx xxxx sample. | |||||||||||
B. compute xxx mean xx xxxxxxxxxxxx xx xxxxxx means and the xxxxxxxxxx mean. xxxxxxx the xxx xxxxxxx | |||||||||||
Solution: | |||||||||||
No. xx Possible xxxxxx | x | C | n | x | x | x | x | (For without replacement | |||
= | 10 | ||||||||||
xxxxxx No. | xxx xxxxxxxx xxxxxxx | Sample xxxx (x) | |||||||||
1 | x | , | x | x | |||||||
x | 2 | , | x | 3 | |||||||
x | x | x | 4 | x | |||||||
4 | 2 | x | 8 | 5 | |||||||
5 | 2 | , | x | 3 | |||||||
x | x | x | 4 | 3 | |||||||
Sample xxx | 7 | x | , | x | 5 | ||||||
x | 4 | , | x | 4 | |||||||
9 | 4 | , | 8 | 6 | |||||||
10 | x | , | x | x | |||||||
Total | xx | ||||||||||
xxxxxx distribution of x xx | x | f | xx | ||||||||
x | x | x | |||||||||
3 | 4 | 12 | |||||||||
x | 1 | x | |||||||||
x | x | xx | |||||||||
x | 2 | 12 | |||||||||
Total | 10 | 40 | |||||||||
xxxxxx mean = | x | ||||||||||
Population mean x x | 2 | x | x | x | 4 | x | x | + | 8 | ) / | x |
4 | |||||||||||
Population means xxx sample means xxx xxxxx | |||||||||||
xx xxxxxxx the xxxxxxxxxx in the xxxxxxxxxx xxxx that of xxx xxxxxx means. | |||||||||||
x | 8 | x | x | ||||||||
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6. x population xxxxxxxx of the xxxxxxxxx five xxxxxxx 2,2,4,4 xxx 8. A. xxxx all samples xx xxxx x and xxxxxxx xxx mean xx xxxx xxxxxxx
xxxxxxx xx size 2 are
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | xxxxxxxxxx from xxxx xxx | Square xx difference | |
2,2 | 2 | xx | 4 |
2,4 | 3 | -1 | 1 |
2,4 | 3 | -1 | x |
xxx | x | x | 1 |
2,2 | 2 | xx | x |
xxx | 3 | xx | x |
2,4 | x | -1 | 1 |
xxx | 5 | 1 | x |
xxx | 3 | xx | x |
xxx | x | -1 | x |
4,4 | 4 | x | 0 |
4,8 | 6 | 2 | x |
4,2 | 3 | xx | 1 |
xxx | x | -1 | 1 |
4,4 | 4 | x | x |
4,8 | x | x | x |
8,2 | x | 1 | 1 |
8,2 | x | 1 | 1 |
xxx | x | 2 | x |
8,4 | 6 | x | x |
xx xxxxxxxx xxx xxxx xx xxxxxxxxxxxx of sample means xxx xxx xxxxxxxxxx xxxxx xxxxxxx xxx two xxxxxxx
Mean xx xxxxxxxxxxxx of sample means xx called xxxxxxxx xxxxx of X. it is xxxxx xx the xxxxxx
∑sample mean= xxxxx xx
Population mean xx xxxxxxxxxx
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xx A population consists xx the following five xxxxxxx xxxxxxx xxx 8. A. List xxx xxxxxxx of size 2 xxx compute the xxxx of each xxxxxxx
xxxxxxx xx size 2 are
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxmean | Difference xxxx mean xxx | xxxxxx of xxxxxxxxxx | |
xxx | 2 | xx | 4 |
xxx | x | -1 | x |
xxx | x | -1 | 1 |
2,8 | 5 | x | x |
xxx | x | -2 | 4 |
xxx | 3 | -1 | x |
2,4 | x | -1 | x |
2,8 | 5 | x | 1 |
xxx | 3 | xx | x |
4,2 | 3 | -1 | x |
xxx | 4 | x | x |
xxx | 6 | 2 | 4 |
4,2 | 3 | -1 | x |
xxx | 3 | -1 | x |
xxx | x | x | x |
xxx | x | x | 4 |
xxx | 5 | 1 | 1 |
8,2 | x | x | x |
xxx | 6 | x | x |
8,4 | 6 | 2 | 4 |
B. xxxxxxxx xxx xxxx xx distribution of sample means xxx xxx xxxxxxxxxx mean. Compare xxx two xxxxxxx
Mean xx distribution of xxxxxx xxxxx is called expected value xx xx xx is xxxxx in the xxxxxx
∑xxxxxx mean= xxxxx =4
xxxxxxxxxx mean xx 2+2+4+4+8=
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