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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

The personnel department wants to estimate the cost of hiring a new secretary.The following data are collected on 8 new secretaries:Estimate the average cost of hiring. Construct a 90 % confidence
A large mail-order company wants to find the effect of sending catalogs to potential customers. Of the 600 potential customers who have just received the new catalogs, 123 responded with an order
The dean of student activities wants to estimate the average spending on beer per week by a student. From a previous study, the standard deviation of spending was estimated to be $39. If the dean
The dean of student activities wants to know students’ reaction to the new student center. Of the 500 students queried, 350 report that they like the new building. Estimate the proportion of the
In question 85, if the dean wants to narrow the 90 % confidence interval to ±1 %, how many students should he ask?Question 85The dean of student activities wants to estimate the average spending on
A soft drink producer installs a new assembly line to fill 12-oz soda cans.After a week of operation, the plant manager randomly samples 120 cans of soda and weighs the soda. He finds that the soda
In question 87, what is the 95 % confidence interval for the variance of the soda pumped into the cans?Question 87A soft drink producer installs a new assembly line to fill 12-oz soda cans.After a
Construct a 90 % confidence interval to estimate the average late time.In an airline company, a committee was formed to study the seriousness of late arrivals of freight. The following report was
Construct a 90 % confidence interval to estimate the percentage of late arrivals.In an airline company, a committee was formed to study the seriousness of late arrivals of freight. The following
Construct a 90 % confidence interval to estimate the standard deviation of late time.In an airline company, a committee was formed to study the seriousness of late arrivals of freight. The following
A potential candidate in the third borough conducted a poll to decide whether he should challenge the incumbent. From a previous poll, he knows that the current incumbent has the support of 45% of
Compute the average cost of 1 repair. Construct an 80 % confidence interval.An automobile manufacturer wants to study the repair record of its own cars. The performance of 1,000 cars and their
Compute the average number of repairs for each car. Construct an 80 % confidence interval.An automobile manufacturer wants to study the repair record of its own cars. The performance of 1,000 cars
Construct a 90 % confidence interval for the standard deviation of costs.An automobile manufacturer wants to study the repair record of its own cars. The performance of 1,000 cars and their
Construct a 90 % confidence interval for the proportion of trouble-free cars.What is the error margin?An automobile manufacturer wants to study the repair record of its own cars. The performance of
Define the following:(a) Convenience lot(b) Single-sampling plan(c) Double-sampling plan(d) Upper control limit(e) Lower control limit(f) Acceptance sampling
Discuss the similarities and differences among X̅-charts, R̅-charts, S-charts, and P-charts.
Thirty samples of 100 items each were inspected, and 68 were found to be defective. Compute control limits for a P-chart.
The following table gives the fraction defective for an automotive piston for 20 samples. Three hundred units are inspected each day. Construct a P-chart and interpret the results. Sample 1 2 23
One hundred insurance forms are inspected daily over 25 working days, and the numbers of forms with errors are recorded below. Construct a P-chart. Day 1 2 3 4 5678 9 10 11 12 13 Number Defective 4
The monthly incomes (in $1,000) from a random sample of eight workers in a factory are 4.2, 5.1, 7.8, 6.2, 8.2, 5.5, 6.7, and 9.1. Assume the population has a normal distribution. Give your answer
A machine produces parts used in cars. A sample of 25 parts was taken. The average length in the sample was 15.95 in. with a sample variance of 0.4 in..(a) Construct a 95 % confidence interval for
For each of the following, test the indicated hypothesis. (a) n = 16, x = 1,550, s4 = 12, Ho: = 1,500, : > 1,500, = .01 (b) n = 9, x = 10.1, s = .81, Ho: = 12, : + 12, = .05 (c) n = 49, x = 17,
A production process is considered in control if no more than 3 % of the items produced are defective. Samples of size 500 are used for the inspection process.(a) Determine the standard error of the
The estimated variance based on 4 measurements of a spring tension was .25 g.The mean was 37 g. Test the hypothesis that the true value is 35 g. Use α = .10 and H1: μ > 35.
A population has a variance σ2 of 100. A sample of 25 from this population had a mean equal to 17. Can we reject H0: μ = 21 in favor of H1: μ ≠ 21? Let α = .05.
Suppose a sample of 15 rulers from a given supplier has an average length of 12.04 in. and the sample standard deviation is .015 in.. If α is .02, can we conclude that the average length of the
The drained weights, in ounces, for a sample of 15 cans of fruit are given below. At a 5 % level of significance, use MINITAB to test the hypothesis that on average a 12-oz drained-weight standard is
An advertisement for a brand-name camera stated that the cameras are inspected and that “60 % are rejected for the slightest imperfections.” To test this assertion, you observe the inspection of
A 1984 study indicated that the average yearly housing cost for a family of 4 was $12,983. A random sample of 200 families in a US city resulted in a mean of $ 14,039 with a standard deviation of
The data entry operation in a large computer department claims that it gives its customers a turnaround time of 6.0 h or less. To test this claim, one of the customers took a sample of 36 jobs and
The following data represent the time, in seconds, that it took the sand in a sample of timers to run out. At the 10 % significance level, can we conclude that the mean for timers of this type is not
Independent random samples from normal populations with the same variance gave the results shown in the following table. Can we conclude that the difference between the means, μ1–μ2, is less than
What is hypothesis testing? Why are we interested in hypothesis testing? In hypothesis testing, is it possible to prove a hypothesis true?
What are the types of errors that can be made in hypothesis testing? Which type of error is generally regarded as more serious?
For each of the following pairs of hypotheses, explain what the null hypothesis should be.(a) Not guilty versus guilty in a court case.(b) Cage is safe versus cage is unsafe when testing the safety
Compare a one-tailed test with a two-tailed test. Give some examples wherein a one-tailed test is preferable to a two-tailed test. Give some examples wherein a two-tailed test is preferable to a
Briefly explain what is meant by the power of a test. Why is the power of the test important?
What is a simple hypothesis? What is a composite hypothesis? Give some examples of a simple hypothesis. Give some examples of a composite hypothesis.
In 1981, the election for governor of the state of New Jersey in which Tom Kean defeated Jim Florio was so close that Florio demanded a recounting of the votes. If you were Florio and you were
In conducting a hypothesis test, how do we determine the rejection region?
Briefly explain why the central limit theorem is important in hypothesis testing.
Evaluate the following statement: “If we reject the null hypothesis that μ= μ0 in a two-tailed test, we will also reject it in a one-tailed test (using the same α).”
You are given the information X̅ = 10, σ = 2, and n = 35. Conduct the following hypothesis test at the .05 level of significance: Ho = 0 versus H >0
Use the information given in question 23 to testat the .05 level of significance.Question 23You are given the information X̅ = 10, σ = 2, and n = 35. Conduct the following hypothesis test at the
You are given the information X̅ = 150, σ = 30, and n = 20. Conduct the following hypothesis test at the .01 level of significance:H0: μ = 100 versus H1: μ > 100
Of 500 students in a high school, 72 % have indicated that they are interested inattending college. What is the probability of selecting a random sample of50 students wherein the sample proportion
The mean interest rate of 500 money market mutual funds is 7.98 % with astandard deviation of 1.01 %. Suppose you draw a sample of 25 mutual funds.(a) What is the mean of the sample mean rate?(b)
Please use the sample means and variances of the above six financial variables in 2011 as an estimate of the population means and variances of the year 2012, and answer the following question:What is
In a survey by the United Airlines of 100 flights between Jan. 2, 2012 to Feb. 15, 2012, whether the flights arrive their destination on time or not are recorded. What is the sample proportion?
Use the results you got in question 85 to plot sample means against sample standard deviation. What is the probability of the range, the sample means between .45 and .55, and the sample standard
Use MINITAB to draw histograms for both the sample means and the sample standard deviations, which have been calculated in question 85. Explain the results.Question 85The MINITAB output in the figure
Suppose you draw two cards from a standard 52-card deck with replacement.Write out the sampling distribution for the suit drawn.
The MINITAB output in the figure is 20 random samples drawn from a uniform distribution between 0 and 1. Calculate the sample means and sample standard deviations by using the MINITAB program. MTB
In a game, a player rolls two dice and counts how many points he gets between them. Write out the sampling distribution.
What are the expected value and standard deviation of the random variable generated in question 79?Question 79In a game, a player rolls two dice and counts how many points he gets between them. Write
The company in question 76 further claims that only 2 % of the cups contain more than half the fat of regular yogurt. What is the probability of our seeing more than 12 cups out of 400 (which is what
On the basis of your answer to question 76, do you believe the advertisement is accurate?Question 76A natural food company is marketing a new yogurt that it advertises as having only half the fat of
A natural food company is marketing a new yogurt that it advertises as having only half the fat of regular yogurt. The average amount of fat in a cup of regular yogurt is 1 unit. The Food and Drug
Suppose the sampling distribution of a sample mean that was developed from a sample of size 40 has a mean of 20 and a standard deviation of 10. Assuming that the population exhibits a normal
Recently the State Education Department of New Jersey wanted to determine the competence in math of the state’s fourth-grade students. Assume that 20 % of the students are actually incompetent in
Assume that 80%of the employees are union members, whereas 20%are not. In the last year, 100 of 500 employees were randomly selected to receive a working bonus. If the company does not discriminate
A cigarette manufacturer came up with a new brand of cigarettes called Long Life. The nicotine content of the cigarettes follows a normal distribution with a mean of 20 and a standard deviation of 5.
Table 8.5 shows the probability distribution of X for n = 2. Show that the average of the random variable X is 3.5. What is the standard deviation of X?Table 8.5 X 1.5 2 2.5 3 3.5 4 4.5 5 5.5 P(X)
Assume the tips received by five waitresses in a given weeknight are $25, $27, $28, $29, and $30. We draw two numbers randomly and take the average. Write the probability distribution of the sample
In a big university, 70 % of the faculty members like to give plus and minus grades (such as B plus and C minus). The other 30 % of the faculty members do not like the plus and minus system. The
The newly produced 1992 Honda boasts 45 miles per gallon on the highway. Assume that the distribution of the miles per gallon is a normal distribution with a mean of 40 and a standard deviation of 5.
The National Treasury Bank wants to approve, at random, two of five loan applications that have been submitted. The loan amounts are $5,000, $8,000, $9,000, $10,000, and $12,000. Obtain the sampling
Assume that the amount of milk in a 16-oz bottle follows a normal distribution with a mean of 16 and a standard deviation of 1. A consumer protection agency bought 30 bottles of milk and weighed
In a local factory, 20 % of the assembly line workers make $5 per hour and 80 % earn $8 per hour. The union computes the mean hourly wage by randomly drawing five workers. Write the sampling
Write out the sampling distribution for rolling a die and flipping a coin.
Suppose you play a game in which you flip three coins. If the flip is a head, you receive 1 point; if the flip is a tail, you receive 2 points. Write out the sampling distribution. What are the
Use the information given in question 7 to find P(3 ≤ X ≤ 7).Question 7Suppose a random variable X can take on only values in the range from 2 to 10 and that the probability that the variable
Suppose a random variable X can take on only values in the range from 2 to 10 and that the probability that the variable will assume any value within any interval in this range is the same as the
Briefly discuss how mean, variance, skewness, kurtosis, and the coefficient of variation can be used to analyze stock rates of return.
Briefly discuss how F statistics can be used to test the difference between two sample variances.
W is a normally distributed random variable with mean 0 and variance 1, and V is a w2-distributed random variable with degrees of freedom (n - 1). How can both t and F distributions be defined in
X is normally distributed, and the sample variance s2 = 20 is calculated from 20 observations. Calculate E(s2) and Var(s2).
Briefly discuss the relationship between the Poisson distribution and the exponential distribution.
Briefly discuss the cumulative distribution function of the uniform distribution presented in Fig. 9.2.Fig. 9.2 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 P(X x) TT 0 A 5 B 10 15 D 20 Se
What is the probability that the sample proportion of negative ROAs is greater than 0.2 in 2012?Please use the sample means and variances of the above six financial variables in 2011 as an estimate
What is the sample proportion of the ROAs of the 37 companies that are negative in 2011?Please use the sample means and variances of the above six financial variables in 2011 as an estimate of the
What is the probability that the sample mean of ROA of the 37 companies is greater than - 1.5 but less than 4.5 in 2012?Please use the sample means and variances of the above six financial variables
Suppose a real estate broker in Albany, New York, is interested in the average price of a home in a development comprising 100 homes.(a) If she uses 12 homes to predict the average price of all 100
Explain the benefits of graphs over tables in presenting data.
Use the EPS and DPS data given in Table 2.3 in Chap. 2 to construct frequency distributions. Table 2.3 Johnson Year DPS 1988 1.89 1989 1.10 1990 1.29 1991 1.51 1992 0.88 1993 1.00 1994 1.12 1995
On November 17, 1991, the Home News of central New Jersey used the bar chart in the accompanying figure to show the 1980–1991 passenger traffic trends for Newark International Airport.(a) Use these
An advertising executive is interested in the age distribution of the subscribers to Person magazine. The age distribution is as follows:(a) Use a frequency distribution graph to present these
Use the data from question 13 to produce a cumulative frequency graph and a cumulative relative frequency graph.Question 13An advertising executive is interested in the age distribution of the
Group the data given in the table into the following groups: $351,000–400,000;401,000–450,000; 451,000–500,000; 501,000–550,000; 551,000–600,000;601,000–650,000; 651,000–700,000; over
Use your results from question 16 to construct a cumulative frequency table.Use the goaltenders’ salaries for the 1991 NHL season given in the following table to answer question.Question 16Group
Use your results from question 16 to construct a relative frequency table and a cumulative relative frequency table.Use the goaltenders’ salaries for the 1991 NHL season given in the following
Use a bar graph to plot the frequency distribution.Use the goaltenders’ salaries for the 1991 NHL season given in the following table to answer question. Name Patrick Roy Ed Belfour Ron Hextall
Construct a cumulative frequency table for the tally table you constructed in question 23.Question 23Use the data given in question 22 to construct a tally table for the grades. Use intervals
Use the data in question 24 to graph the cumulative frequency on a bar chart by using Microsoft Excel.Question 24Construct a cumulative frequency table for the tally table you constructed in question
Construct a cumulative frequency table.Use the following information to answer question. Suppose a class of high school seniors had the following distribution of SAT scores in English. SAT score
Use a histogram to graph the cumulative frequencies.Use the following information to answer question. Suppose a class of high school seniors had the following distribution of SAT scores in English.
Construct a frequency polygon.Use the following information to answer question. Suppose a class of high school seniors had the following distribution of SAT scores in English. SAT score 401-450
Compute the relative frequencies and the cumulative relative frequencies.Use the following information to answer question. Suppose a class of high school seniors had the following distribution of SAT
Construct a relative frequency histogram.Use the following information to answer question. Suppose a class of high school seniors had the following distribution of SAT scores in English. SAT score

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