BGA 501 ASSIGNMENT 2 SOLUTION

Question: #1274

Suppose that a government agency wants to estimate the average number of kids per family in California. A random sample of 120 families in California reveals that the sample mean of number of kids is 2.7 per family, with a sample standard deviation of 0.7. Compute a 99.7% confidence interval to estimate the population mean.

A researcher is interested in estimating the average purchase amount for convenience stores. To do so, she randomly sampled 32 purchases from several convenience stores and tabulated the amounts to the nearest dollar. Use the following data to construct a 95% confidence interval for the population average amount of purchase:

$2	$11	$8	$7
5	4	2	1
14	7	9	3
4	3	3	8
9	3	1	6
10	8	5	4
7	5	3	9
6	4	7	12

The National Automobile Dealers Association collects data on sales numbers, prices, and usage of both new and used automobiles. One statistic of interest is the percentage of automobiles that are still on the road after 10 years ( U.S. News & World Report, September 9, 1991). A random sample of 1000 cars were selected in 1991.

a) Assume that 27% of automobiles sampled in 1991 were still on the road after 10 years. Provide a 95% confidence interval for the population proportion. What is your interpretation of this confidence interval?

b) How large a sample should be taken if we want to be 95% confident that the sample percentage is within 2.5% of the actual percentage of automobile that are still on the road after 10 years?

A real estate company wishes to estimate, with 95 percent confidence, the difference between the average rental prices of two-bedroom apartments in two cities, San Diego (City 1) and San Francisco (City 2). A random sample of 60 apartment complex is taken from each city. The sample mean prices equal $680 for City 1 and $700 for City 2; the sample standard deviations are $55 and $67 for City 1 and 2, respectively.

a) From the given information, can you tell us which city has a higher average rental price at 95% confidence? Explain.

b) If the answer in a) is inconclusive, what should you do in order to obtain a conclusive solution at the same confidence level?

Schumacher is a supplier of high purity chemicals to the semiconductor industry. Most of Schumacher’s products are used for the manufacture of integrated circuit chips. Because of the extremely high complexity and numerous process steps, Schumacher must always provide consistent product to its customers. A project has been initiated to study incoming raw material quality and how it effects the final product. In this problem we focus on two major materials used by the company, called Component A and B. Two random samples, one for component A, the other for Component B were collected by the analytical department. The result is shown in the following table. The reason for the small number of data points is that previously this product was manufactured in R&D Department on small scale. Large batch processing has just been started. Since sample sizes are not large enough, we will assume that the distribution of putity is indeed normal.

	Purity (%)
	Comp. A	Comp. B
1	99.46	98.8
2	99.47	99.45
3	99.54	99.45
4	99.64	99.53
5	99.62	99.53
6	99.75	99.63
7	99.68	99.61
8	99.69	99.12
9	99.93	99.54
10	99.51	99.12
11	99.67	99.54
12	99.62	99.51
13	99.62	99.52
14	99.67	99.17
15	99.63
16	99.68

Use Minitab to construct separate 99% confidence intervals of the average purity for Component A and B.

Use Minitab to construct the 99% confidence interval for the difference of the two population means. Can you indicate which component, A or B, has higher average purity?

The city manager wants to compare the average rental prices of the coastal and inland areas of her city. The rental prices of randomly selected coastal 2-bedroom apartments and inland 2-bedroom apartments in her city are obtained and stored in two columns named COAST and INLAND in a Minitab file “Rental.mtw” (it’s in the course website under Data Files).

Construct a 95% confidence interval of the difference of the average rental prices of the two areas using the formula in the text. You can use Minitab to compute certain statistics needed for your calculation. At 95% confidence can you tell the manager what area has higher average rental price? By how much?
Use Minitab to construct the 95% confidence interval of the difference of the average rental prices of the two areas. Is the result the same as the one calculated in a)? If it were different, would it change your answers to those questions listed in a)?

The Vallecitos Water District is a public agency that provides water and wastewater treatment and disposal in the greater San Marcos area. The resident population in the service is approximately 55,500. During the drought years of 1980’s and early 1990’s, the District implemented demand management pricing strategies as part of its conservation program. A project was conducted to compare the water consumption in single family residences in base year 1989/90 to consumption in 1995/96. The management hoped there was a decrease in the volume of water consumed since the implementation of the District'’ conservation strategy. The months of July, August, and September were chosen as these months frequently represent the period of peak annual consumption.

Forty seven (47) single family residences were randomly selected. Their water consumptions in the three months of 1989 and 1995 were entered into two columns as shown below.

Family	Total-89	Total-95
1	59	74
2	47	48
3	14	64
4	49	61
5	35	12
6	56	69
7	158	135
8	41	43
.	.	.
.	.	.
.	.	.

The unit is 100 cubic feet, which is equal to 748 gallons. For example, the first family in the sample consumed 5,900 cubic feet of water in 1989 for the months of July, August, and September, and 7,400 cubic feet in the same period of 1995. The second family consumed 4,700 in 1989 in the same period, and so forth. The data file is called Water-usage.mtw (it’s in the course website under Data Files).

Answer the following questions.

Find the mean, median, and standard deviation of water consumptions for both years.
Does water consumption follow a normal distribution? Use Minitab/Excel to draw frequency distributions of the two variables to answer this question. Can you explain why the distribution has its form?
Find the 95% confidence intervals for the average water consumptions for the two years.
Find the 95% confidence interval for the difference of the average water consumptions of the two years. Do you see a clear difference of the two years?

Solution: #1251

BGA 501 Assignment 2 SOLUTION

For the given data, the sample statistics are calculated and stated as follows:
The sample size, ...