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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

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
Construct a cumulative 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.
Construct a tally table for the closing stock prices “Close” column. Use 1,000-point intervals beginning with 301–1,300, 1,301–2,301, etc.Use the following prices of Swiss stocks to answer
Compute the change in prices by subtracting the previous closing price from the current closing price.Use the following prices of Swiss stocks to answer question. Switzerland (in Swiss francs) 1.
Use your answer to question 43 to construct a tally table. Use 30-point intervals beginning with -120 ~ -91,–90 ~ -61, etc.Use the following prices of Swiss stocks to answer question.Question
Use your answer to question 44 to compute the cumulative frequencies.Use the following prices of Swiss stocks to answer question.Question 44Use your answer to question 43 to construct a tally table.
Use your answer to question 44 to compute the relative and cumulative relative frequencies.Use the following prices of Swiss stocks to answer question.Question 44Use your answer to question 43 to
Use your answer to question 46 to graph the relative frequency.Use the following prices of Swiss stocks to answer question.Question 46Use your answer to question 44 to compute the relative and
Use your answer to question 46 to graph the cumulative frequency.Use the following prices of Swiss stocks to answer question.Question 46Use your answer to question 44 to compute the relative and
Create a frequency polygon using data from question 44.Use the following prices of Swiss stocks to answer question.Question 44Use your answer to question 43 to construct a tally table. Use 30-point
Refer to Table 2.5, in which the balance sheet of JNJ company for the year 2008 and 2009 are given. Draw the pie chart of the composition of the total current asset of JNJ for the year 2008 and 2009,
What is your mean speed if you drive 35 miles per hour for 2 h and 55 miles per hour for 3 h?
Carefully explain the difference between a population and a sample.Why is the formula we use to calculate the population standard deviation different from the one we use to calculate the sample
A quality control manager finds the following number of defective light bulbs in 10 cases of light bulbs:(a) Draw a frequency diagram for the class intervals 0–2 3–5 6–8 9 and over(b) Draw a
Use the data given in question 23 of Chap. 2 to compute the mean, standard deviation, and coefficient of variation for(a) The exchange rate between dollars and pounds.(b) The exchange rate between
(a) Use the 3-month T-bill rate and prime rate information given in Table 4.16 to calculate the Z score.(b) Use this information on Z score to do related analysis.Table 4.16 Year 90 91 92 93 94 95 96
Use the data given in Table 3.9 to compute the mean, standard deviation, coefficient of variation, and coefficient of skewness for the current ratio of JNJ.Table 3.9 Year 1990 1991 1992 1993 1994
Repeat question 39 using the current ratio data for MRK.Question 39Use the data given in Table 3.9 to compute the mean, standard deviation, coefficient of variation, and coefficient of skewness for
You are given the following information about two stocks:(a) Calculate the mean and standard deviation for each stock.(b) Compare the mean, standard deviation, and coefficient of variation of each
Calculate the skewness coefficient for the data given in question 42.The following information is for questions 44–52. The following table gives the current ratio and inventory turnover for
The following information is for question. The following table gives the current ratio and inventory turnover for Chrysler, Ford, GM, and the auto industry from 1969 to 1990:Compute the mean,
Using a calculator and the MINITAB program, answer questions 45–46 and 48–49 again, using the data for GM.Questions 46Compute the mean, variance, and coefficient of variation for Chrysler’s
Answer questions 45–46 and 48–49 again, using the data for the auto industry.Questions 46Compute the mean, variance, and coefficient of variation for Chrysler’s current ratio for the period
Refer to Table 2.3, in which data on EPS, DPS, and PPS for JNJ, Merck, and S&P 500 during the period 1988–2009 are given.Table 2.3Please calculate the standard deviation for EPS, DPS, and PPS
Suppose school records reveal that historically, 10 % of the students in Milton High School have dropped out of school. What is the probability that more than two students in a class of 30 will drop
Again consider the car sales rep in question 67. What is the probability that she will make at least two sales after speaking to four customers?Question 67A car sales representative sees an average

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