1. Thirty-two small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 40.9 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.

As the confidence level increases, the margin of error increases.    

As the confidence level increases, the margin of error remains the same.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.

As the confidence level increases, the confidence interval increases in length.    

As the confidence level increases, the confidence interval remains the same length.

2. Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 40 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.50 ml/kg for the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is large

the distribution of weights is normal

σ is known

σ is unknown

the distribution of weights is uniform

(c) Interpret your results in the context of this problem.

1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.   

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.

99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.70 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)
_____ male firefighters

3. Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 10 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.32 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is large

uniform distribution of weights

σ is known

normal distribution of weights

σ is unknown

(c) Interpret your results in the context of this problem.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.    

There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.14 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

5) Thirty-five small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 44.9 cases per year. (a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit upper limit margin of error (b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit upper limit margin of error (c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit upper limit margin of error (d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase? As the confidence level increases, the margin of error increases. As the confidence level increases, the margin of error remains the same. As the confidence level increases, the margin of error decreases. (e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length? As the confidence level increases, the confidence interval increases in length. As the confidence level increases, the confidence interval remains the same length. As the confidence level increases, the confidence interval decreases in length.

1) The Bay of Fundy-Passamaquoddy area near the border between Maine and New Brunswick/Nova Scotia in Canada, is another prime site for tidal power. The basin area is 700km² and the average tidal range is 10.8 meters. Calculate the theoretical maximum power generating capability and the estimated realistic power available from this site. (SHOW your WORK)

2) A client wants you to design a roof-mounted solar water heater to supplement the energy input to their radiant floor heating system. They would like to have an indirect solar collection system similar to the one shown in Figure 11.16 of your textbook. The south-facing solar collector has a stated efficiency of 41%, and will be used to INDIRECTLY heat water in a supplemental storage tank that has a capacity of 150 Liters (~ 40 gallons). The circulating pump will operate at the rate of 20 x 10^-6 m³/sec. On a typical summer day, there are 5.6 hours of direct sunshine, which creates a 15.5°C temperature rise in the solar collector fluid for that whole time period. Assume the collector fluid is water (heat capacity of 4.184 J/g-°C). What will be the increase in temperature of the water in the storage tank?

1) The Bay of Fundy-Passamaquoddy area near the border between Maine and New Brunswick/Nova Scotia in Canada, is another prime site for tidal power. The basin area is 700km² and the average tidal range is 10.8 meters. Calculate the theoretical maximum power generating capability and the estimated realistic power available from this site. (SHOW your WORK)

2) A client wants you to design a roof-mounted solar water heater to supplement the energy input to their radiant floor heating system. They would like to have an indirect solar collection system similar to the one shown in Figure 11.16 of your textbook. The south-facing solar collector has a stated efficiency of 41%, and will be used to INDIRECTLY heat water in a supplemental storage tank that has a capacity of 150 Liters (~ 40 gallons). The circulating pump will operate at the rate of 20 x 10^-6 m³/sec. On a typical summer day, there are 5.6 hours of direct sunshine, which creates a 15.5°C temperature rise in the solar collector fluid for that whole time period. Assume the collector fluid is water (heat capacity of 4.184 J/g-°C). What will be the increase in temperature of the water in the storage tank?

Thirty-two small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 43.7 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

Thirty-two small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 44.5 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.

As the confidence level increases, the margin of error increases.    

As the confidence level increases, the margin of error remains the same.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.

As the confidence level increases, the confidence interval remains the same length.    

As the confidence level increases, the confidence interval increases in length.

Fairfield Homes is developing two parcels near Pigeon Forge, Tennessee. In order to test different advertising approaches, it uses different media to reach potential buyers. The mean annual family income for 13 people making inquiries at the first development is $151,000, with a standard deviation of $41,000. A corresponding sample of 28 people at the second development had a mean of $183,000, with a standard deviation of $28,000. Assume the population standard deviations are the same. At the 0.10 significance level, can Fairfield conclude that the population means are different?

1. State the decision rule for 0.10 significance level: H₀: μ₁ = μ₂; H₁:μ₁ ≠ μ₂. (Negative values should be indicated by a minus sign.Round your answers to 2 decimal places.)

2. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Thirty-one small communities in Connecticut (population near 10,000 each) gave an average of x(with a dash above it) = 138.5 reported cases of larceny per year. Assume that σ is known to be 42.7 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

Thirty-five small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 41.1 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit =

upper limit =

margin of error =

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit =

upper limit =

margin of error =

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit =

upper limit =

margin of error =

Problem 07-8AA Merchandising: Preparation of a complete master budget LO P4

Near the end of 2019, the management of Dimsdale Sports Co., a merchandising company, prepared the following estimated balance sheet for December 31, 2019.

To prepare a master budget for January, February, and March of 2020, management gathers the following information.

1. The company’s single product is purchased for $20 per unit and resold for $57 per unit. The expected inventory level of 5,000 units on December 31, 2019, is more than management’s desired level, which is 20% of the next month’s expected sales (in units). Expected sales are January, 6,500 units; February, 9,250 units; March, 11,500 units; and April, 10,500 units.
2. Cash sales and credit sales represent 25% and 75%, respectively, of total sales. Of the credit sales, 57% is collected in the first month after the month of sale and 43% in the second month after the month of sale. For the December 31, 2019, accounts receivable balance, $125,000 is collected in January 2020 and the remaining $395,000 is collected in February 2020.
3. Merchandise purchases are paid for as follows: 20% in the first month after the month of purchase and 80% in the second month after the month of purchase. For the December 31, 2019, accounts payable balance, $65,000 is paid in January 2020 and the remaining $295,000 is paid in February 2020.
4. Sales commissions equal to 20% of sales are paid each month. Sales salaries (excluding commissions) are $60,000 per year.
5. General and administrative salaries are $144,000 per year. Maintenance expense equals $2,000 per month and is paid in cash.
6. Equipment reported in the December 31, 2019, balance sheet was purchased in January 2019. It is being depreciated over eight years under the straight-line method with no salvage value. The following amounts for new equipment purchases are planned in the coming quarter: January, $38,400; February, $91,200; and March, $24,000. This equipment will be depreciated under the straight-line method over eight years with no salvage value. A full month’s depreciation is taken for the month in which equipment is purchased.
7. The company plans to buy land at the end of March at a cost of $180,000, which will be paid with cash on the last day of the month.
8. The company has a working arrangement with its bank to obtain additional loans as needed. The interest rate is 12% per year, and interest is paid at each month-end based on the beginning balance. Partial or full payments on these loans can be made on the last day of the month. The company has agreed to maintain a minimum ending cash balance of $42,000 at the end of each month.
9. The income tax rate for the company is 43%. Income taxes on the first quarter’s income will not be paid until April 15.

Required:
Prepare a master budget for each of the first three months of 2020; include the following component budgets.

6. Monthly cash budgets.
7. Budgeted income statement for the entire first quarter (not for each month).
8. Budgeted balance sheet as of March 31, 2020.