Questions and Answers of Statistics For Business And Economics

Suppose Incheon, a city in South Korea, has 500 real estate agents. The mean value of the properties sold in a year by these agents is $550,000, and the standard deviation is $200,000. A random
Suppose that we have a population with proportion P = 0.30 and a random sample of size n = 200 drawn from the population.a. What is the probability that the sample proportion is greater than 0.28?b.
Suppose that we have a population with proportion P = 0.20 and a random sample of size n = 100 drawn from the population.a. What is the probability that the sample proportion is greater than 0.18?b.
Suppose that we have a population with proportion P = 0.55, and a random sample of size n = 150 drawn from the population.a. What is the probability that the sample proportion is more than 0.60?b.
Suppose that we have a population with proportion P = 0.30, and a random sample of size n = 900 drawn from the population. a. What is the probability that the sample proportion is more than
Suppose that 80% of all tax returns in your country lead to a refund. A random sample of 100 tax returns is taken.a. What is the mean of the distribution of the sample proportion of returns leading
A record store owner finds that 20% of customers entering her store make a purchase. One morning 180 people, who can be regarded as a random sample of all customers, enter the store.a. What is the
Ahead of the 2019 Indian general election, a random sample of 100 voters is taken to estimate the proportion of a state’s electorate in favor of increasing the fuel tax to provide additional
A company wants to estimate the proportion of people who are likely to purchase electric shavers from those who watch the FIFA World Cup. A random sample obtained information from 150 people who were
Suppose that in Europe, 55% of all adults believe that a major overhaul of the economy’s health care delivery system is essential. What is the probability that more than 65% of a random sample of
Seong-Un is a local fishery in Busan, the second mostpopulous city in South Korea. In 2017, an employee survey conducted by Seong-Un found that 55% of its employees were concerned about future health
Consider a normally distributed population with a population mean of μ = 100 and a variance of σ2 = 40.a. What is the probability that the sample variance is greater than 70 when n = 17?b.
Monthly rates of return on the shares of a particular common stock are independent of one another and normally distributed with a standard deviation of 2.2.A sample of 12 months is taken.a. Find the
The number of hours spent watching Netflix by students in the week before their final exams has a normal distribution with a standard deviation of 5 hours. A random sample of 41 students was taken.a.
A production process manufactures electronic components with timing signals whose duration follows a normal distribution. A random sample of nine components was taken, and the durations of their
Each member of a random sample of 16 business economists was asked to predict the rate of inflation for the coming year. Assume that the predictions for the whole population of business economists
What is meant by the statement that the sample mean and the sample proportion have a sampling distribution? What other statistical examples can you provide?
There are six white-collar workers at a university department with the following ages:56, 38, 29, 58, 43, 47Two of the workers are to be chosen at random.a. How many possible samples of two workers
Of what relevance is the central limit theorem to the sampling distribution of the sample means?
A quality-control manager was concerned about variability in the amount of an active ingredient in diarrhea pills produced by a particular process. A random sample of 26 pills was taken. What is the
A sample of 200 students is to be taken to determine which of two brands of fruit juice (A and B) is preferred in a blind taste test. Suppose that, in the whole population of students, 60% would
A dependent random sample from two normally distributed populations gives the following results:a. Find the 98% confidence interval for the difference between the means of the two populations.b. Find
A random sample of six salespeople who attended a motivational course on sales techniques was monitored 3 months before and 3 months after the course. The table shows the values of sales (in
Independent random sampling from two normally distributed populations gives the following results:Find a 99% confidence interval estimate of the difference in the means of the two populations. nx =
Scores on a particular test, taken by a large group of students, follow a normal distribution with a variance of 2500. A random sample of 25 scores was taken to estimate the population’s mean
A manufacturer of liquid detergent claims that the mean weight of liquid in containers sold is at least 50 ounces. It is known that the population distribution of weights is normal with a standard
In a particular year 1/3 of home sales were partially financed by the seller. A random sample of 300 sales is examined.a. The probability is 0.9 that the sample proportion is more than what amount?b.
Independent random sampling from two normally distributed populations gives the following results:Find a 95% confidence interval estimate of the difference between the means of the two populations.
A candidate for office intends to campaign in a state if her initial support level exceeds 30% of the voters. A random sample of 500 voters is taken, and it is decided to campaign if the sample
It is known that the incomes of subscribers to a particular British magazine have a normal distribution with a variance of 49,000,000. A random sample of 41 subscribers is taken.a. What is the
Determine the margin of error for a 95% confidence interval for the difference between population means for each of the following (assume equal population variances):a.b.c. The sample sizes in part a
Batches of chemical are manufactured by a production process. Samples of 30 batches from a production run are selected for testing. If the standard deviation of the percentage of impurity contents in
A manufacturer knows that the number of items produced per hour by machine A and by machine B are normally distributed with a standard deviation of 4.6 items for machine A and a standard deviation of
In January 2019, the Lufthansa Innovation Hub (LIH) enetered its first collaboration with INSEAD, Singapore. Collaborative learning is a good driver of growth in the current global market. Suppose
Brämhults Juice, based in Sweden, produces chilled fruit and vegetable juices. A manager at Brämhults is considering purchasing a new machine to bottle 16-fluid-ounce (473-milliliter) bottles of
Happy Heart, Inc., a Norwegian company, offers health care and nutritional services for parents. It uses Birth Season to define when a baby is born 11 = spring/summer; 2 = autumn/winter2 and Walking
Independent random samples from two normally distributed populations give the following results:Assume that the unknown population variances are equal and find a 90% confidence interval for the
Suppose that for a random sample of 250 firms that revalued their fixed assets, the mean ratio of debt to tangible assets was 0.625 and the sample standard deviation was 0.176. For an independent
Independent random samples from two normally distributed populations give the following results:If we do not assume that the unknown population variances are equal, what is the 99% confidence
A researcher intends to estimate the effect of a drug on the scores of human subjects performing a task of psychomotor coordination. The members of a random sample of 9 subjects were given the drug
In randomized, double-blind clinical trials of a new medical supplement, test subjects were randomly divided into two groups. The people in Group X received the new supplement while those in Group Y
Would you use your school library more if the hours were extended? From a random sample of 121 freshmen, 75 indicated that they would use the school’s library more if the hours were extended. In an
Supermarket shoppers were observed and questioned immediately after putting an item in their cart. Of a random sample of 220 choosing a product at the regular price, 137 claimed to check the price
A proposal for a new 1-cent tax increase to support cancer research is to appear on the ballot in one county’s next election. The residents in Hangzhou and Chengdu, two cities in China, were
The Baby Walking data file contains information concerning the birth, first steps, age, and so on for 98 babies. The variable “siblings” refers to the number of siblings the baby has, and the
A newspaper article reported that 350 people in one state were surveyed and 60% were opposed to a recent court decision. The same article reported that a similar survey of 550 people in another state
A random sample of 15 employees in a large manufacturing plant found the following figures for number of hours of overtime worked in the last month: 24 16 17 18 21 17 16 19 19 24 15 19 18 21 24
There is concern about the speed of automobiles traveling over a particular stretch of highway. For a random sample of 28 automobiles, radar indicated the following speeds, in miles per hour:a. Check
A random sample of 10 homes in a particular suburb had the following selling prices (in thousands of pounds):a. Check for evidence of nonnormality.b. Find a point estimate of the population mean that
A random sample of 10 economists produced the following forecasts for percentage unemployment rate in the next year:a. The population meanb. The population variancec. The variance of the sample
The Taiwan Real Estate data file contains information on several variables related to houses sold in Taiwan in 2012 and 2013. Build an appropriate 90% confidence interval to check if there has been a
The Taiwan Real Estate data file contains information on several variables related to houses sold in Taiwan in 2012 and 2013. Build an appropriate 95% confidence interval to compare the age of the
The demand for bottled water increases during the hurricane season in Florida. The operations manager at a plant that bottles drinking water wants to be sure that the filling process for 1-gallon
Find the reliability factor, Za/2, to estimate the mean, m, of a normally distributed population with known population variance for the following.a. 81% confidence levelb. 86% confidence levelc. 80%
Find the reliability factor, zα/2, to estimate the mean, μ, of a normally distributed population with known population variance for the following.a. a = 0.09b. α/2 = 0.01
Assume a normal distribution with known population variance. Calculate the margin of error to estimate the population mean for the following.a. 99% confidence level; n = 81; σ2 = 169b. 90%
Assume a normal distribution with known population variance. Calculate the width to estimate the population mean, μ, for the following.a. 90% confidence level; n = 100; σ2 = 169b. 95% confidence
Build Rental is a plant hire company in the United Kingdom that provides machinery, equipment, and tools for a limited period to construction contractors. It is interested in the amount of time its
Assume a normal distribution with known population variance. Calculate the LCL and UCL for each of the following.a. x = 255; n = 304; σ = 30; α = 0.01b. x = 395; n = 105; σ2 = 100; α = 0.05c. x =
How much do students pay, on an average, for textbooks during the first semester of college? From a random sample of 250 students from the Corvinus University of Budapest, Hungary, the mean cost was
Calculate the confidence interval to estimate the population proportion for each of the following.a. 90% confidence level; n = 700; p = 0.20b. 99% confidence level; n = 140; p = 0.01c. α = 0.03; n =
Suppose that a random sample of 126 graduate-admissions personnel from Finland was asked what role scores on standardized tests (such as the GMAT or GRE) play in the consideration of a candidate for
A statistician at the Nagoya University, Japan, was assessing the number of students’ résumés with false or misleading information. Suppose the students of the university were asked if such a
Consider the following random sample from a normal population:11 17 8 7 9a. Find the 90% confidence interval for population variance.b. Find the 95% confidence interval for the population variance.
Pegatron Corporation, a Taiwanese electronics manufacturing company, is concerned about the variability of the levels of impurity contained in consignments of raw material from a supplier. A random
A watch manufacturer in Switzerland uses sputtered titanium coating for some models it creates. A random sample of nine observations on the thickness of this coating is taken from a week’s output,
Assume simple random sampling. Calculate the variance of the sample mean, σ2x , for each of the following.a. N = 1,300; n = 100; s = 15b. N = 1,500; n = 200; s2 = 91c. N = 3,000; n = 220; s2 = 150
Assume simple random sampling. Calculate the 95% confidence interval estimate for the population mean for each of the following.a. N = 1600; n = 80; s = 10; x = 144b. N = 1575; n = 70; s2 = 64; x =
Assume simple random sampling. Calculate the confidence interval for the population total for each of the following.a. N = 1,500; n = 200; s = 25; x = 100; 90% confidence levelb. N = 2,000; n = 250;
Assume simple random sampling. Calculate the confidence interval for the population proportion, P, for each of the following.a. N = 1,675; n = 400; x = 120; 99% confidence levelb. N = 955; n = 100; x
Take a random sample of 80 pages from this book and estimate the proportion of all pages that contain mathematical formulas.
Axion Revisionsbyrå, a Swedish accounting firm, employs 268 junior accountants. In a random sample of 49 of these, the mean number of hours overtime billed in a particular week was 7.6, and the
An auditor, examining a total of 830 accounts receivable of a corporation, took a random sample of 80 of them. The sample mean was €129.19, and the sample standard deviation was €43.11.a. Using
On a particular day Citizens Advice, a consumer-advice bureau in London, received 215 calls. For a random sample of 49 of these calls, it was found that the mean time taken in providing the requested
The county finance department in Exercise 7.90 also wants information about renewals of disabled parking placards. Suppose that in a sample of 430 transactions for disabled parking placards, it was
For each of the following statements, add the word wider or narrower so that they are true.a. For a given number of population members and a given sample variance, the larger the number of sample
A senior manager, responsible for a group of 150 junior executives, is interested in the total amount of time per week spent by these people in internal meetings. A random sample of 36 of these
A simple random sample of 200 from a total 1,380 colleges in a country maintained that 18 colleges use the text Statistics Made Difficult and Boring. Find a 95% confidence interval for the proportion
The dean of The Business School of Auckland University, New Zealand, is contemplating proposing a change in the requirements for graduation. At present, business majors are required to take one
An accounting firm has 1,200 clients. From a random sample of 121 clients, 110 indicated very high satisfaction with the firm’s service. Find a 95% confidence interval for the proportion of all
A class has 270 students. The final examination is optional – taking it can raise, but cannot lower, a student’s grade. Of a random sample of 45 students, 27 indicated that they would take the
How large of a sample is needed to estimate the mean of a normally distributed population for each of the following?a. ME = 2; s = 39; a = 0.05b. ME = 4; s = 39; a = 0.05c. Compare and comment on
How large a sample is needed to estimate the population proportion for each of the following?a. ME = 0.03; a = 0.05b. ME = 0.05; a = 0.05c. Compare and comment on your answers to parts a and b.
Determine the sample size needed for each of the following situations.a. N = 1,950; σ = 600; 1.96σx = 75b. N = 1,950; σ = 600; 1.96σx = 150c. N = 1,950; σ = 600; 1.96σx =
Determine the sample size needed for each of the following situations.a. N = 1,000; σ = 450; 1.96σx = 50b. N = 3,000; σ = 450; 1.96σx = 50c. N = 1,000,000; σ = 450; 1.96σx = 50d. Compare and
Determine the sample size needed for each of the following situations.a. N = 5,000; p = 0.5; 1.96σp = 0.10b. N = 5,000; p = 0.5; 1.96σp = 0.05
The mean amount of the 1,560 mortgages taken out in Vienna, Austria, in the past year must be estimated. Based on previous experience, a real estate broker knows that the population standard
An automobile dealer has an inventory of 500 used cars. To estimate the mean mileage of this inventory, she intends to take a simple random sample of used cars. Previous studies suggest that the
The Vikla Golf and country club, Cyprus, wants to poll a random sample of its 560 members to estimate the proportion likely to attend an early-season function. The number of sample observations
Consider the data in Exercise 7.90. Suppose that we computed for the population proportion who pay for vehicle registration by mail a confidence interval extending from 0.15 to 0.17. What is the
Consider the data in Exercise 7.90. It was reported in the local paper that almost two-thirds (from 57% to 63%) of the population prefers the online renewal process. What is the confidence level of
The Weibull distribution is often used in engineering studies to model the random lifetime of a device. It is a right-skewed distribution and can be generated with the RiskWeibull function. This
Play Things is developing a new Miley Cyrus doll. The company has made the following assumptions:• The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is
The file P17_10.xlsx contains customer data on acceptance of products with various attributes. This is explained more fully in the file. There are three potential Yes/No dependent variables, Acceptl,
The file P17_22.xlsx contains the following data on 84 people: annual income, amount invested in the stock market, and a 0-1 variable on whether they subscribe to the Wall Street Journal.a. Use
The file P17_23.xlsx contains data on 80 (fictional) houses, including their selling prices, although the selling price is missing for the first house. It turns out that when the dependent variable
This problem (originally created by Palisade) is a test of a neural net’s ability to learn. The file P17_24.xlsx contains data on three numbers, two operations, and two results. The first two
The sample space S = [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11] . Given A = [E5, E6, E7, E8] and B = [E5, E7, E9, E11]a. What is A intersection B?b. What is the union of A and B?c. Is the union
Given A = [E1, E4, E5, E7] and B = [E2, E3, E5, E8]a. What is A intersection B?b. What is A intersection B?c. What is the union of A and B?d. Is the union of A and B collectively exhausted?
Given A = [E3, E5, E7, E10] and B = [E3, E4, E5, E9]a. What is the intersection of A and B?b. What is the union of A and B?c. Is the union of A and B collectively exhaustive?

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