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mathematics
statistics

Questions and Answers of Statistics

Construct a histogram of the PCKnowledge variable. Repeat this separately for those who own a PC and those who do not. Then find a 95% confidence interval for the mean value of PCKnowledge for all of
SoftBus believes it can afford to spend much less time with customers who own PCs and score at least 4 on PCKnowledge. Let’s call these the “PC-savvy” customers. On the other hand, SoftBus
Following up on the previous problem, SoftBus believes its profit from each prospective customer depends on the customer’s level of PC knowledge. It divides the customers into three classes:
Find a 95% confidence interval for the proportion of customers who will purchase at least one item if they receive a coupon for 5% off. Repeat for 10% off and for 15% off.
Find a 95% confidence interval for the proportion of customers who will purchase at least one item and pay at least $500 total if they receive a coupon for 5% off. Repeat for 10% off and for 15% off.
Comfy wonders whether there are differences across pairs of cities that receive the same discount. a. Find a 95% confidence interval for the difference between the mean amount spent in Tucson and the
Find a 95% confidence interval for the proportion of customers who purchase the extended service plan. Find a 95% confidence interval for the proportion of all customers who would benefit by
Find a 95% confidence interval for Niyaki’s mean net warranty cost per unit sold (net of the $50 paid for the plan for those who purchase it). You can assume that this mean is for the first failure
This problem follows up on the previous two problems with the data in the Data2 sheet of the file. Here Niyaki did more investigation on the same 70 customers. It tracked subsequent failures and
The file P08_77.xlsx contains data on 856 customers who have either tried or not tried a company’s new frozen lasagna dinner. The manager of the company would like to compare the proportion of
The formula for a 95% confidence interval for a mean is so well-rooted in statistical theory and practice that you might not even consider other possibilities. However, many researchers and even
Harrigan University is a liberal arts university in the Midwest that attempts to attract the highest quality students, especially from its region of the country. It has gathered data on 178
The Snow Pea Restaurant is a Chinese carryout/delivery restaurant. Most of Snow Pea’s deliveries are within a 10-mile radius, but it occasionally delivers to customers more than 10 miles away. Snow
Ralph Butts, manager of Woodland Operations for Intergalactica Papelco’s Southeastern Region, had to decide this morning whether to approve the Bodfish Lot logging contract that was sitting on his
The file P09_01.xlsx contains a random sample of 100 light bulb lifetimes. The company that produces these light bulbs wants to know whether it can claim that its light bulbs typically last more than
A manufacturer is interested in determining whether it can claim that the boxes of detergent it sells contain, on average, more than 500 grams of detergent. The firm selects a random sample of 100
A producer of steel cables wants to know whether the steel cables it produces have an average breaking strength of 5000 pounds. An average breaking strength of less than 5000 pounds would not be
A U.S. Navy recruiting center knows from past experience that the heights of its recruits have traditionally been normally distributed with mean 69 inches. The recruiting center wants to test the
Suppose that you wish to test H0: µ = 10 versus Ha: µ > 10 at the α = 0.05 significance level.Furthermore, suppose that you observe values of the sample mean and sample standard deviation when n =
A study is performed in a large southern town to determine whether the average weekly grocery bill per four-person family in the town is significantly different from the national average. A random
An aircraft manufacturer needs to buy aluminum sheets with an average thickness of 0.05 inch. The manufacturer knows that significantly thinner sheets would be unsafe and considerably thicker sheets
Suppose that you observe a random sample of size n from a normally distributed population. If you are able to reject H0: µ = µ0 in favor of a two-tailed alternative hypothesis at the 10%
In the past, 60% of all undergraduate students enrolled at State University earned their degrees within four years of matriculation. A random sample of 95 students from the class that matriculated in
Suppose a well-known baseball player states that, at this stage of his career, he is a “300 hitter” or better. That is, he claims that he gets a hit in at least 30% of his at-bats. Over the next
The director of admissions of a distinguished (i.e., top-20) MBA program is interested in studying the proportion of entering students in similar graduate business programs who have achieved a
A market research consultant hired by a leading soft drink company wants to determine the proportion of consumers who favor its low-calorie drink over the leading competitor’s low-calorie drink in
The CEO of a medical supply company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He claims that the proportion of women in similar
Management of a software development firm would like to establish a wellness program during the lunch hour to enhance the physical and mental health of its employees. Before introducing the wellness
The managing partner of a major consulting firm is trying to assess the effectiveness of expensive computer skills training given to all new entry-level professionals. In an effort to make such an
A large buyer of household batteries wants to decide which of two equally priced brands to purchase. To do this, he takes a random sample of 100 batteries of each brand. The lifetimes, measured in
The managers of a chemical manufacturing plant want to determine whether recent safety training workshops have reduced the weekly number of reported safety violations at the facility. The management
A real estate agent has collected a random sample of 75 houses that were recently sold in a suburban community. She is particularly interested in comparing the appraised value and recent selling
The owner of two submarine sandwich shops located in a particular city would like to know how the mean daily sales of the first shop (located in the downtown area) compares to that of the second shop
Suppose that an investor wants to compare the risks associated with two different stocks. One way to measure the risk of a given stock is to measure the variation in the stock’s daily price
A manufacturing company wants to determine whether there is a difference between the variance of the number of units produced per day by one machine operator and the similar variance for another
A large buyer of household batteries wants to decide which of two equally priced brands to purchase. To do this, he takes a random sample of 100 batteries of each brand. The lifetimes, measured in
Do undergraduate business students who major in finance earn, on average, higher annual starting salaries than their peers who major in marketing? Before addressing this question through a
The CEO of a medical supply company is committed to expanding the proportion of highly qualified women in the organization’s large staff of salespersons. Given the recent hiring practices of his
The director of admissions of a top-20 MBA program is interested in studying the proportion of entering students in similar graduate business programs who have achieved a composite score on the
Managers of a software development firm have established a wellness program during the lunch hour to enhance the physical and mental health of their employees. Now, they would like to see whether the
An Environmental Protection Agency official asserts that more than 80% of the plants in the northeast region of the United States meet air pollution standards. An antipollution advocate is not
A television network decides to cancel one of its shows if it is convinced that less than 14% of the viewing public are watching this show.a. If a random sample of 1500 households with televisions is
An economic researcher wants to know whether he can reject the null hypothesis, at the 10% significance level, that no more than 20% of the households in Pennsylvania make more than $70,000 per year.
Senior partners of an accounting firm are concerned about recent complaints by some female managers that they are paid less than their male counterparts. In response to these charges, the partners
Do undergraduate business students who major in finance earn, on average, higher annual starting salaries than their peers who major in marketing? Address this question through a statistical
The file P02_35.xlsx contains data from a survey of 500 randomly selected households. Test for the existence of a significant difference between the mean debt levels of the households in the first
Elected officials in a Florida city are preparing the annual budget for their community. They want to determine whether their constituents living across town are typically paying the same amount in
Suppose that you sample two normal populations independently. The variances of these two populations are σ21 and σ22. You take random samples of sizes n1 and n2 and observe sample variances of s21
Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. Quality control personnel inspect a random sample of the teams’ assemblies and judge each assembly to be
A market research consultant hired by a leading soft drink company is interested in determining whether there is a difference between the proportions of female and male consumers who favor the
The employee benefits manager of a large public university wants to determine whether differences exist in the proportions of various groups of full-time employees who prefer adopting the second
The file P02_35.xlsx contains data from a survey of 500 randomly selected households. Researchers would like to use the available sample information to test whether home ownership rates vary by
For testing the difference between two proportions is used as the approximate standard error of p̂1 - p̂2, where p̂c is the pooled sample proportion. Explain why this is reasonable when the
The file P02_11.xlsx contains data on 148 houses sold in a certain suburban region.a. Create a histogram of the selling prices. Is there any visual evidence that the distribution of selling prices is
The file P09_33.xlsx contains real estate taxes paid by a sample of 170 homeowners in a Florida city. a. Create a histogram of the taxes paid. Is there any visual evidence that the distribution of
The file P09_42.xlsx contains many years of monthly percentage changes in the Dow Jones Industrial Average (DJIA). a. Create a histogram of the percentage changes in the DJIA. Is there any visual
The file P09_45.xlsx contains measurements of ounces in randomly selected cans from a soft-drink filling machine. These cans reportedly contain 12 ounces, but because of natural variation, the actual
The file P08_49.xlsx contains data on 400 orders placed to the ElecMart Company over a period of several months. For each order, the file lists the time of day, the type of credit card used, the
The file P08_18.xlsx categorizes 250 randomly selected consumers on the basis of their gender, their age, and their preference for our brand or a competitor’s brand of a low-calorie soft drink. Use
The file P02_11.xlsx contains data on 148 houses that were recently sold. Two variables in this data set are the selling price of the house and the number of bedrooms in the house. We want to use a
The file P03_50.xlsx contains annual salaries for all NBA basketball players in each of five seasons. a. Using only the data for the most recent season (2008–2009), check whether there is
The file P09_51.xlsx contains data on 1000 randomly selected Walmart customers. The data set includes demographic variables for each customer as well as their salaries and the amounts they have spent
The file DVD Movies.xlsx (the file that accompanies the case for Chapter 7) contains data on close to 10,000 customers from several large cities in the United States. The variables include the
An automobile manufacturer employs sales representatives who make calls on dealers. The manufacturer wishes to compare the effectiveness of four different call-frequency plans for the sales
Consider a large chain of supermarkets that sells its own brand of potato chips in addition to many other name brands. Management would like to know whether the type of display used for the store
National Airlines recently introduced a daily early morning nonstop flight between Houston and Chicago. The vice president of marketing for National Airlines decided to perform a statistical test to
How powerful is the ANOVA test in detecting differences between means when you are sure that there are differences? You can explore this question with simulation. Use the generic formula
The file P09_57.xlsx contains the number of days 44 mothers spent in the hospital after giving birth (in the year 2005). Before health insurance rules were changed (the change was effective January
Eighteen readers took a speed-reading course. The file P09_58.xlsx contains the number of words that they could read before and after the course. Test the alternative hypothesis at the 5%
Statistics have shown that a child 0 to 4 years of age has a 0.0002 probability of getting cancer in any given year. Assume that during each of the last seven years there have been 100 children ages
African Americans in a St. Louis suburb sued the city claiming they were discriminated against in schoolteacher hiring. Of the city’s population, 5.7% were African American; of 405 teachers in the
In the past, monthly sales for HOOPS, a small software firm, have averaged $20,000 with standard deviation $4000. During the most recent year, sales averaged $22,000 per month. Does this indicate
Twenty people have rated a new beer on a taste scale of 0 to 100. Their ratings are in the file P09_62.xlsx. Marketing has determined that the beer will be a success if the average taste rating
Twenty-two people were asked to rate a competitive beer on a taste scale of 0 to 100. Another 22 people were asked to rate our beer on the same taste scale. The file P09_63.xlsx contains the results.
Callaway is thinking about entering the golf ball market. The company will make a profit if its market share is more than 20%. A market survey indicates that 140 of 624 golf ball purchasers will buy
Sales of a new product will be profitable if the average of sales per store exceeds 100 per week. The product was test-marketed for one week at 10 stores, with the results listed in the file
A recent study concluded that children born to mothers who take Prozac tend to have more birth defects than children born to mothers who do not take Prozac. a. What do you think the null and
The file P02_16.xlsx contains traffic data from 256 weekdays on four variables. Each variable lists the number of arrivals during a specific five-minute period of the day. Use one-way ANOVA to test
Suppose that you are the state superintendent of Tennessee public schools. You want to know whether decreasing the class size in grades 1 through 3 will improve student performance. Explain how you
A group of 25 husbands and wives were chosen randomly. Each person was asked to indicate the most he or she would be willing to pay for a new car (assuming each had decided to buy a new car). The
A company is concerned with the high cholesterol levels of many of its employees. To help combat the problem, it opens an exercise facility and encourages its employees to use this facility. After a
Suppose that you are trying to compare two populations on some variable (GMAT scores of men versus women, for example). Specifically, you are testing the null hypothesis that the means of the two
This problem concerns course scores (on a 0–100 scale) for a large undergraduate computer programming course. The class is composed of both underclassmen (freshmen and sophomores) and upperclassmen
A cereal company wants to see which of two promotional strategies, supplying coupons in a local newspaper or including coupons in the cereal package itself, is more effective. The company randomly
There is a lot of concern about “salary compression” in universities. This is the effect of paying huge salaries to attract newly-minted Ph.D. graduates to university tenure-track positions and
Each year drinking and driving behavior are estimated to be responsible for approximately 24,000 traffic fatalities in the United States. Data show that a preponderance of this problem is due to the
John Jacobs works for the Fresh Toothpaste Company and has recently been assigned to investigate a new type of toothpaste dispenser. The traditional tube of toothpaste uses a screw-off cap. The new
For years, the drug Vioxx, developed and marketed by Merck, was one of the blockbuster drugs on the market. One of a number of so-called Cox-2 anti-inflammatory drugs, Vioxx was considered by many
Explore the relationship between the selling prices (Y) and the appraised values (X) of the 148 homes in the file P02_11.xlsx by estimating a simple linear regression model. Interpret the standard
The file P02_10.xlsx contains midterm and final exam scores for 96 students in a corporate finance course. Each row contains the two exam scores for a given student, so you might expect them to be
A company produces electric motors for use in home appliances. One of the company’s production managers is interested in examining the relationship between inspection costs in a month (X) and the
The owner of the Original Italian Pizza restaurant chain wants to understand which variable most strongly influences the sales of his specialty deep-dish pizza. He has gathered data on the monthly
The human resources manager of DataCom, Inc., wants to examine the relationship between annual salaries (Y) and the number of years employees have worked at DataCom (X). These data have been
The file P02_02.xlsx contains information on over 200 movies that came out during 2006 and 2007. a. Create two scatter plots and corresponding correlations, one of Total US Gross (Y) versus 7-day
Examine the relationship between the average utility bills for homes of a particular size (Y) and the average monthly temperature (X). The data in the file P10_07.xlsx include the average monthly
The file P10_08.xlsx contains data on the top 200 professional golfers in 2009. a. Create a new variable, Earnings per Round, and the ratio of Earnings to Rounds. Then create five scatter plots and
Management of a home appliance store wants to understand the growth pattern of the monthly sales of Blu-ray disc players over the past two years. The managers have recorded the relevant data in the
Do the selling prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the
The file P10_11.xlsx contains annual observations of the American minimum wage since 1955. Has the minimum wage been growing at roughly a constant rate over this period? Use simple linear regression
Based on the data in the file P02_23.xlsx from the U.S. Department of Agriculture, explore the relationship between the number of farms (X) and the average size of a farm (Y) in the United States.

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