Liberty University BUSI 230 week 5 exercises 6.4-7.3 complete solutions answers and more!

Liberty University BUSI 230 week 5 exercises 6.4-7.3 complete solutions answers and more!

Question 1

What is a population parameter?

A population parameter is a     descriptive measure of a    .

Answer

Give three examples. (Select all that apply.)

Question 2

What is a sample statistic?

A     descriptive measure of a     .

Answer

Give three examples. (Select all that apply.)

Question 3

List two unbiased estimators and their corresponding parameters. (Select all that apply.)

Question 4

Suppose x has a distribution with a mean of 90 and a standard deviation of 36. Random samples of size n = 64  are drawn.

(a) Describe the x distribution and compute the mean and standard deviation of the distribution

x has     distribution with mean μx =      and standard deviation σx =     .

Answer

(b) Find the z value corresponding to x = 99.

(c) Find P(x < 99). (Round your answer to four decimal places.)

P(x < 99) =

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 99? Explain.

Question 5

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 56 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 56 tons and standard deviation σ = 1.2 ton.

(a) What is the probability that one car chosen at random will have less than 55.5 tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that 19 cars chosen at random will have a mean load weight x of less than 55.5 tons of coal? (Round your answer to four decimal places.)

(c) Suppose the weight of coal in one car was less than 55.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

Suppose the weight of coal in 19 cars selected at random had an average x of less than 55.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?

Question 6

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 7600 and estimated standard deviation σ = 2550. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

What is the probability of x < 3500? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

Question 7

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 52.0 kg and standard deviation σ = 7.8 kg. Suppose a doe that weighs less than 43 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)

(b) If the park has about 2500 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 49 kg. If the average weight is less than 49 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than 49 kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability that x < 53.1 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)

Suppose park rangers captured, weighed, and released 40 does in December, and the average weight was x = 53.1 kg. Do you think the doe population is undernourished or not? Explain.

Question 8

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 12 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 = 0.26 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.)

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

(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.)

Question 9

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken twelve blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.85 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. 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.)

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

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.20 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)

Question 10

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.90 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.37 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.) 

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

Question 11

Thirty-three 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?

(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?

Question 12

Use the Student's t distribution to find tc for a 0.95 confidence level when the sample is 24. (Round your answer to three decimal places.)

Question 13

As the degrees of freedom increase, what distribution does the Student's t distribution become more like?

Question 14

How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)

Question 15

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)

Question 16

Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to two decimal places.)

(b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (Round your answer to two decimal places.)

(c) Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain.

Question 17

What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports from eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):

Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean percentage x and the sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 90% confidence interval for the population average μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)

Question 18

You want to conduct a survey to determine the proportion of people who favor a proposed tax policy. How does increasing the sample size affect the size of the margin of error?

Question 19

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 61 professional actors, it was found that 45 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

Answer

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

Give a brief interpretation of the meaning of the confidence interval you have found.

Answer

(c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

Question 20

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5670 physicians in Colorado showed that 3251 provided at least some charity care (i.e., treated poor people at no cost).

(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)

Answer

(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

Give a brief explanation of the meaning of your answer in the context of this problem.

Answer

(c) Is the normal approximation to the binomial justified in this problem? Explain.

Question 21

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Case studies showed that out of 10,494 convicts who escaped from certain prisons, only 8005 were recaptured.

(a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (Round your answer to four decimal places.)

Answer

(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

Give a brief statement of the meaning of the confidence interval.

Answer

(c) Is use of the normal approximation to the binomial justified in this problem? Explain.

Question 22

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 20 out of 857 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish.

(a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p. (Round your answer to four decimal places.)

Answer

(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

Give a brief explanation of the meaning of the interval.

Answer

(c) Is the normal approximation to the binomial justified in this problem? Explain.

Question 23

A random sample of 340 medical doctors showed that 164 had a solo practice.

(a) Let p represent the proportion of all medical doctors who have a solo practice. Find a point estimate for p. (Use 3 decimal places.)

Answer

(b) Find a 90% confidence interval for p. (Use 3 decimal places.)

Give a brief explanation of the meaning of the interval.

Answer

(c) As a news writer, how would you report the survey results regarding the percentage of medical doctors in solo practice?

Answer

What is the margin of error based on a 90% confidence interval? (Use 3 decimal places.)