Calculating Confidence Intervals

5. You have decided to find a new one-bedroom apartment to live in. You want to find an apartment no further than a 30 miles from EKU. Using Zillow you take a random sample of 61 apartments. The mean rent of the sample is 640 dollars and the standard deviation 55 dollars. You want to use 95% confidence interval for the mean monthly rent for one-bedroom apartments within 30 miles of EKU to get an idea of how much on average people spend. Confirm that the sample size is large enough, calculate a 95% confidence interval and interpret the interval. (Round your answer to 2 decimal places)

6. Using the information in question 5 calculate a 95% interval assuming you sampled 10 apartments instead of 30. You do not need to check the sample size or interpret the interval. (Round your answer to 2 decimal places

7. Using the information in question 5 calculate a 95% interval assuming you sampled 101 apartments instead of 30. You do not need to check the sample size or interpret the interval. (Round your answer to 2 decimal places)

8. Compare your answers from questions 5-7. What happens to a confidence interval when the sample size changes but everything else remains the same?

1. a. Calculate the number of pounds of CO₂ produced from a weekend trip to San Fransisco. Assume 275 miles one-way and an average fuel efficiency of 22 miles per gallon. Assume gasoline to be pure octane (C₈H₁₈) with a density of .70 g/mL. (Hint: start your work by writing out the balanced equation for the combustion of octane.)

b. A past electric bill showed that my housegold used 380 Kwh (kilowatt-hours) of power over a period of a month. If a Kw is equal to a kJ/s (kilojoule per second) and the enthalpy (heat) of combustion of octane (deltaH_comb.)= - 5980 kJ/mol (C₈H₁₈), calculate the number of moles of octane that it would take to make this electricity. Convert the moles of octane into pounds of CO₂. (Although power plants do not use octane to make electricity, other reduced carbon fuels are common. Also, we must remember that the conversion of chemical energy within the power plant to electrical energy and its delivery to your household outlet is a process that is, at best, 40% efficient. Factor this efficiency into your final answer.)

c. Compare your answers from Part A and Part B. What can you conclude about the amount of energy needed to take a "day trip down the coast" and the energy necessary to live in a house for a month? Explain.

Background: As you know there is a high pressure region in the center of the Pacific called the North Pacific high. This high pressure region is responsible for the clockwise rotating geostrophic flow in the North Pacific called the North Pacific gyre. Locally, we call this current the California current.

Theory:

a) A typical atmospheric pressure difference between the center of the North Pacific high and its edge 1000 nautical miles away is 10-20 millibar.

- Assume that the pressure gradient is linear and estimate the horizontal pressure gradients caused by this pressure difference. Give you answer in Pascal/meter.

- Compute the geostrophic currents resulting from this pressure difference in m/s and knots.

b) Due to the Coriolis force once the North Pacific gyre starts moving, water curves towards the center of the gyre. This water accumulates and increases the sea surface height at the center of the gyer by as much as 1-2 meters above the exterior of the gyre which may be 1000 nautical miles from the center.

- Use the usual relationship between sea surface height and pressure to convert this height difference to a pressure difference.

- Assume that the pressure gradient is linear and estimate the horizontal pressure gradients caused by this pressure difference. Give you answer in Pascal/meter.

- Compute the geostrophic currents resulting from this pressure difference in m/s and knots.

5

Which analysis tool that we studied (from the bulleted list below) should one use for each situation listed in a through d below? Also, state the null and alternative hypothesis for each situation.

a. Testing to see if a brand of tires marketed as lasting 60,000 miles does last 60,000 miles. Your sample size is 100 tires.

b. Testing to see if the failures recorded for these tires follow an exponential distribution.

c. Testing to see if samples of Firestone and Goodyear 60,000-mile tires have the same life. Your sample size is 15 Firestone and 20 Goodyear tires.

d. Testing two brands of tires to see if the age of the driver affects the number of gallons of gas used on a 500-mile trip for five different age groups of drivers.

Choose the best tool to apply to each test (a-d) from the list below.

Z-test / Normal distribution one sample versus threshold(s)

Z-test comparison of two samples T-Test one sample versus threshold(s)

T-test Two Sample assuming unequal variances

T-test Paired data (dependent samples)

Binomial test of one proportion versus threshold(s)

Binomial Test of two proportions

Chi-Square Contingency Table

Chi-Square Goodness of Fit

The Parker Piano Company purchased a Delivery Truck on January 1, 2025 for $50,000 which included all costs to get the asset ready for use. The truck has an anticipated life of 100,000 miles or 4 years. The estimated residual value at the end of the assets service life is expected to be $2,000. For assets of this type, the company utilizes the straight-line depreciation method.

1. Record the purchase of the asset.

2. Complete the depreciation table below.

3. Record the entry for December 31, 2025 to record the depreciation for the year.

4. Suppose the company sells the van on December 31, 2027 for $18,000 cash. Provide the journal entry to record the sale.

5. Assume the company chooses to use the units-of-production method. Based on the information below, complete the depreciation schedule.

Rent a rideshare bike and ride it throughout the course at a pace that elevates your heartbeat
somewhat, but without over-exertion. Time your ride and calculate your average speed. Draw a
force diagram for the bicycle’s motion, and label it with estimates of each force. Calculate the
power you used during your ride to maintain your average speed, in watts and then in
horsepower. Calculate the (exercise) Calories you burned during your ride. (My time was 8.23 minutes for 1.3 miles)

Rent a rideshare scooter and ride it throughout the same course at a safe speed. Try to go
somewhat faster than the bike, but most importantly stay safe. Time your ride and calculate your
average speed. Draw a force diagram and label it with estimates of each force. Calculate the
power used by the electric motor to maintain your average speed, in watts and then in
horsepower. (My time was 1.2 miles for 11minutes and 10mph.)
In both calculations, include estimates for resistance from both surface friction and air. You will
need to research a plausible (e.g., order of magnitude) estimate for (a) the coefficient of rolling
friction from the wheels (used in the same way as the coefficient of kinetic friction we discuss in
class problems), and (b) drag from air resistance. Which is larger?

MAke sure to calculate air resistance and friction resistance for the bike and scooter. Draw force diagrams for the bike and scooter.

1. Multiple Regression Analysis

The manager of the BuieCreek Police department motor pool wants to develop a forecast model for annual maintenance on police cars, based on mileage in the past year and age of the cars. The following data have been collected for eight different cars:

A. Use Data Analysis in Excel to develop a multiple regression model and answer the following questions.

B.Write regression equation. Is the overall multiple regression result reliable? Explain why or why not by discussing R2 and F test. Notes: Simply mentioning the numbers without elaboration will earn no credit.

C. How would an additional year of car age affect the annual maintenance cost? Increase or decrease? By how much? Is it statistically significant at 5% level? Explain.

D. How would an additional 1000-mile driven affect the annual maintenance cost? increase or decrease? By how much? Is it statistically significant at 5%?

E. Forecast the annual maintenance cost for a police car that is 10 years old and will be driven 20,000 miles in 1 year. Is this forecast reliable? Explain why or why not?

Based on your teams determination of the number of airplanes needed, ExpressJet is considering multiple options for acquiring the Embraer 170 airplanes at a price of $10.9 million each. The executives in charge of capital acquisitions at ExpressJet are relying on you to show and explain which option will place the company in the best financial position based on your Net Present Value calculations. In the past, all acquisitions have been in cash. However with the current trend of the company, the options being considered are as follows:

Calculate Net Present Value for all the scenarios as compared to a cash purchase. Use the below data to fill in the spreadsheet.

Cost of new equipment $10,900,000

Expected life of equipment in years 30

Disposal Value in 5 years $1,090,000

Lifetime miles per plane 1,575,000,000

Annual miles per year 52,500,000

Number of workers needed 3

Annual hours to be worked per employee 2,000

Earnings per hour for employees $35

Annual health benefits per employee $2,000

Other annual benefits per employee -% of wages 15%

Cost per passenger seat mile $0.06

Other variable costs per seat mile $0.10

Cost to purchase cans-per can $0.50

Required rate of return 11%

Taxe Rate 35%

Monthly lease payments $95,000

Lease term 10 years

Monthly Note Payments ($203,208.91)

Note Term 5 years

Down Payment $1,000,000

Kathy Chen​, owner of Flower Hour​, operates a local chain of floral shops. Each shop has its own delivery van. Instead of charging a flat delivery​ fee, Chen wants to set the delivery fee based on the distance driven to deliver the flowers. Chen wants to separate the fixed and variable portions of her van operating costs so that she has a better idea how delivery distance affects these costs. She has the following data from the past seven​ months:

Use Microsoft Excel to run a regression​ analysis, then do the​ following: