## QRB 560 Week 6 1 Heading Suppose we have a finite population

QRB 560 Week 6

Problem 1
Suppose we have a finite population of 1000 people representing a population of a small city. 240 of those people are female white, 260 are male white, 210 are female black, and 290 people are male black.
– Using Excel Sampling, select a random sample of 25 people from this population
– If you select a stratified sample of 30 people from this population, how many of each population category would you select in the sample
– Using Excel Sampling, select a stratified sample of 30 people from this population

Using Excel Sampling, select a stratified sample of 30 people from the population were as followed:

Problem 2

In order to estimate employee time-to-work arrival delays in minutes, a random sample of 40 employees was monitored and values of delay to arrive to work were recorded as shown in Table 1. According to the human resources department, the standard deviation of delay is 10 minutes. Estimate the mean of delay time at 95% and 99% confidence intervals.

Table 1 Delay-to-arrive time values
Employee # Time Delay (min) Employee # Time Delay
(min) Employee # Time Delay (min) Employee # Time Delay (min)
1 10 11 0 21 0 31 5
2 5 12 8 22 7 32 2
3 2 13 3 23 14 33 18
4 13 14 6 24 10 34 32
5 12 15 1 25 8 35 21
6 12 16 2 26 20 36 15
7 14 17 0 27 13 37 12
8 10 18 8 28 18 38 4
9 2 19 5 29 7 39 5
10 4 20 5 30 5 40 17
n=355/40=8.88

Problem 3

In 2007, some statistics revealed that the population of professors in the State of Alabama has an average annual salary of \$80,000 and a standard deviation of \$10,000. The distribution of professor’s salary is a normal distribution. If a random sample of 40 professors was taken in that year and it was found that it has a mean value of \$70,000.
(a) What is the sampling error?
(b) What does the sign of the sampling error mean?
(c) What is the standard error?
(d) Using the empirical rule, do you believe this sample to be representative of the population? Justify your Yes or No answer.
(e) Based on your answer of part (d) do you believe the sampling error calculated in part (a) is a pure sampling error or it may involve non-sampling error?

Problem 4

Lind, Marchal, & Wathen Ch. 18, exercises 27, 28, 33, and 34 (p. 645)
Below is information on food items for the years 2000 and 2004.

27. Compute a simple price index for each of the four items. Use 2000 as the base period.
28. Compute a simple aggregate price index. Use 2000 as the base period.
Betts Electronics purchases three replacement parts for robotic machines used in their manufacturing process. Information on the price of the replacement parts and the quantity purchased is given below.
33. Compute a simple price index for each of the three items. Use 2000 as the base period.
34. Compute a simple aggregate price index for 2004. Use 2000 as the base period.

28. Compute a simple aggregate price index. Use 2000 as the base period.

33. Compute a simple price index for each of the three items. Use 2000 as the base period.

34. Compute a simple aggregate price index for 2004. Use 2000 as the base period.

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