Questions and Answers of Essential Statistics Business

Find the frequency, proportion, and percentage of women in Table 1A on page 27. Table 1A on page 27. The data in Table 1A were collected from one of the authors’ statistics classes. The column
Explain why the variable Male, in Table 1A, is categorical, even though its values are numbers. Often, it does not make sense, or is not even possible, to add the values of a categorical variable.
Suppose you decided to code handedness using Right-handed as the label for the column. How many ones and how many zeros would there be?The data in Table 1A were collected from one of the authors’
Suppose you decided to code eye color using 1 for Brown Eyes and 0 for Not Brown Eyes. What would be the label at the top of the column, and how many ones and zeros would there be?The data in Table
Are the following variables, from Table 1A, numerical or categorical? Explain.a. Handedness b. Age The data in Table 1A were collected from one of the authors’ statistics classes. The
Give an example of another categorical variable we might have recorded for the students whose data are in Table 1A?The data in Table 1A were collected from one of the authors’ statistics classes.
Give an example of another numerical variable we might have recorded for the students whose data are in Table 1A?The data in Table 1A were collected from one of the authors’ statistics classes. The
In Table 1A, there are observations on how many people? The data in Table 1A were collected from one of the authors’ statistics classes. The column heads give the variable, and each of the
Are the following variables, from Table 1A, numerical or categorical? Explain. a. Shoe size b. Eye color The data in Table 1A were collected from one of the authors’ statistics
In Table 1A, how many variables are there?The data in Table 1A were collected from one of the authors’ statistics classes. The column heads give the variable, and each of the other rows represents
What problems are evident in the wording of these two questions? What is your race? What is your religious preference?• White• Christian• Black• Jewish
Households can sign up for a telemarketing “no-call list.” How might households who sign up differ from those who don’t? What biases might this create for telemarketers promoting(a) Financial
A vehicle emissions testing facility can process up to 100 cars in an hour and the facility is open 7 am?5 pm Monday?Thursday. Shown below are the number of cars processed each hour last week. (a)
Small power surges (5–10 volts) occur in a residence an average of 50 times in a 24-hour period.(a) What is the approximate normal probability of at least 60 small power surges in a randomly chosen
Telemarketers use a predictive dialing system to decide whether a person actually answers a call (as opposed to an answering machine). If so, the call is routed to a telemarketer. If no telemarketer
A poll of 125 college students who watch The Big Bang Theory showed that 83 of them usually watch on a mobile device (e.g., laptop).(a) Assuming that this was a random sample, construct a 90 percent
A sample of 40 songs from a student’s iTunes playlist showed a mean length of 3.542 minutes with a standard deviation of 0.311 minute. Construct a 95 percent confidence interval for the population
The average age of a part-time seasonal employee at a Vail Resorts ski mountain has historically been 37 years. State the hypotheses one would use to test if this average has decreased since the last
Determine the p-value for each test statistic.a. Right-tailed test, z = +1.34b. Left-tailed test, z = −2.07c. Two-tailed test, z = −1.69
Is leverage high?(a) hi = .13, n = 16;(b) hi = .13, n =50;(c) hi = .36, n = 100.
Are the variables cross-sectional data or time-series data?
How do you imagine the data were collected?
Are the X and Y data well-conditioned? If not, make any transformations that may be necessary and explain.
Results of a one-year research study of 112 full-time employees in California fast-food establishments are shown in the 2 ? 2 contingency table below. Research question: At ? = .05, was flu incidence
Sixty-four students in an introductory college economics class were asked how many credits they had earned in college and how certain they were about their choice of major. Research question: At ? =
To see whether students who finish an exam first get the same grades as those who finish later, a professor kept track of the order in which papers were handed in. Of the first 25 papers, 10 received
Can people really identify their favorite brand of cola? Volunteers tasted Coke, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At ? = .05, is the correctness of
A survey of randomly chosen new students at a certain university revealed the data below concerning the main reason for choosing this university instead of another. Research question: At ? = .01, is
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 27.0 mpg and a standard
Calculate the standard error of the sample proportion.a. n = 40, π = .30b. n = 200, π = .10c. n = 30, π = .40d. n = 400, π = .03
Guest ages at a ski mountain typically have a right-skewed distribution. Assume the standard deviation (σ) of age is 14.5 years.(a) Even though the population distribution of age is right-skewed,
Should p be assumed normal?a. n = 200, π = .02b. n = 100, π = .05c. n = 50, π = .50
Of 43 bank customers depositing a check, 18 received some cash back.(a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back.(b) Check the normality
The combined city/highway fuel economy of a 2016 Toyota 4Runner 2WD 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range 17 mpg to 22 mpg.(a)
A sample of 40 songs from a student’s iTunes playlist showed a mean length of 3.542 minutes with a standard deviation of 0.311 minute.(a) Construct a 95 percent confidence interval for the mean.(b)
How “decaffeinated” is decaffeinated coffee? If a researcher wants to estimate the mean caffeine content of a cup of Starbucks’ decaffeinated espresso with 98 percent confidence and an error of
A random sample of 30 cans of Del Vino crushed tomatoes revealed a mean weight of 798.3 grams (excluding the juice). The can-filling process for Del Vino crushed tomatoes has a known standard
Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels
Ouranos Resorts would like to send a survey to its guests asking about their satisfaction with the new website design. It would like to have a margin of error of ±5 percent on responses with 95
A manufacturer claims that its compact fluorescent bulbs contain an average of 2.5 mg of mercury. Write the hypotheses for a two-tailed test, using the manufacturer’s claim about the mean as the
The Scottsdale fire department aims to respond to fire calls in 4 minutes or less, on average. State the hypotheses you would use if you had reason to believe that the fire department’s claim is
The Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, wants to use a sample to perform a two-tailed test to see whether the mean incoming metal thickness is at the
According to J.D. Power & Associates, the mean purchase price of a smartphone device (such as an iPhone or Galaxy) in 2016 was $318. In 2017, a random sample of 20 business managers who owned a
May normality of the sample proportion p be assumed? Show your work.a. H0: π = .30 versus H1: π ≠ .30, n = 20b. H0: π = .05 versus H1: π ≠ .05, n = 50c. H0: π = .10 versus H1: π ≠ .10, n
A Realtor claims that no more than half of the homes he sells are sold for less than the asking price. When reviewing a random sample of 12 sales over the past year, he found that actually 10 were
An analyst is considering making one of the following changes to her hypothesis test. Explain how each change would affect P(Type I error), P(Type II error) and power.(a) Changing the sample size n =
If we fail to reject the null hypothesis that π = .50 even though the true proportion is .60, what is the probability of Type I error?
When told that over a 10-year period a mammogram test has a false positive rate of 50 percent, Bob said, “That means that about half the women tested actually have no cancer.” Correct Bob’s
A quality control standard requires that no more than 5 percent of bags of Halloween candy be underweight. A random sample of 200 bags showed that 16 were underweight.(a) At α = .025, is the
The average mpg usage for a 2017 Toyota Prius for a sample of 10 tanks of gas was 45.5 with a standard deviation of 1.8. For a 2017 Ford Fusion, the average mpg usage for a sample of 10 tanks of gas
In 2016, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2017, a sample of the same size showed that 62 paid by debit card.(a) Formulate appropriate hypotheses to test whether
In 2016, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2017, a sample of the same size showed that 62 paid by debit card.(a) Formulate appropriate hypotheses to test whether
Researchers at the Mayo Clinic have studied the effect of sound levels on patient healing and have found a significant association (louder hospital ambient sound level is associated with slower
A ski resort tracks the proportion of seasonal employees who are rehired each season. Rehiring a seasonal employee is beneficial in many ways, including lowering the costs incurred during the hiring
(a) Use Excel?s Data page 470 Analysis > Regression (or MegaStat or Minitab) to obtain regression estimates. (b) Interpret the 95 percent confidence interval for the slope. Does it contain
Calculate the standardized residual ei* and determine whether or not it is unusual or an outlier.(a) ei = 25, se = 8;(b) ei = −15, se = 7;(c) ei = 112, se = 77
Given se = 14, what is the raw residual if the standardized residual is(a) ei* = 2.00;(b) ei* = −1.50;(c) ei* = 0.50.
State the hi cutoff point for “high leverage” when(a) n = 25;(b) n = 40;(c) n = 200.
A binary logistic regression was fitted using a sample of employees of a large corporation to investigate if the employee?s monthly salary (Salary) predicts whether (1) or not (0) the employee has a
Does the number of address changes (Moves) in the last decade predict whether (1) or not (0) a college graduate lacks health insurance (Uninsured)? Use the fitted binary logistic regression to
Is the sample size sufficient to yield a good estimate? If not, do you think more data could easily be obtained, given the nature of the problem?
Use Excel’s Add Trendline feature to fit a linear regression to the scatter plot. Is a linear model credible?
Is an auto-correlation test appropriate for your data? If so, perform an eyeball inspection of residual plot against observation order or a runs test.
Researchers found a correlation coefficient of r = .50 on personality measures for identical twins. A reporter interpreted this to mean that “the environment orchestrated one-half of their
SAT scores are often used as a proxy for how well a state educates the students who reside in that state. However, not all students in a state actually take the SAT, and SAT participation rates vary
(a) Make a line chart for JetBlue?s revenue, using the years as X-axis labels. (b) Click on the line and fit a linear trend to the data (slope, intercept, R2). (c) What does the R2 tell you? The
Below are results of a regression of Y = average stock returns (in percent) as a function of X = average price/earnings ratios for the period 1949?1997 (49 years). Separate regressions were done for
Does a new car owner?s monthly car payment (CarPmt) predict whether (1) or not (0) the owner subscribes to satellite radio (SatRad)? Use the fitted logistic model below to predict the probability of
A ski resort asked a random sample of guests to rate their satisfaction on various attributes of their visit on a scale of 1–5 with 1 = very unsatisfied and 5 = very satisfied. The estimated
Are these cross-sectional data or time-series data? What is the unit of observation (e.g., firm, individual, year)?
Does your sample size fulfill Evans’ Rule (n/k ≥ 10) or at least Doane’s Rule (n/k ≥ 5)?
The actual distribution of car colors for 2006 model car buyers is shown below. Based on the sample of 200 car buyers for 2016 model vehicles, use the multinomial chisquare GOF test at ? = .05 to
Belkins University offers free tuition to faculty dependents. Twelve of the 45 faculty whose dependents qualify for free tuition are using the benefit. A random survey is conducted with eight of the
A car dealership offers a prepaid maintenance plan for their new vehicles that covers all scheduled maintenance for the first three years. The cost of the plan is $499. Jennifer has just purchased a
If Punxsutawney Phil sees his shadow on February 2, then legend says that winter will last 6 more weeks. In 118 years, Phil has seen his shadow 104 times.(a) What is the probability that Phil will
Based on the previous problem, is major independent of gender? Explain the basis for your conclusion.
Based on the reported experience of climbers from a given year, a climber who attempts Everest has a 31 percent chance of success.
More than 30 percent of the results from major search engines for the keyword phrase “ring tone” are fake pages created by spammers.
The probability that a randomly selected student in your class is celebrating a birthday today is 1/365.
The probability of rolling three sevens in a row with dice is .0046.
Commercial rocket launches have a 95 percent success rate.
There is a 25 percent chance that AT&T Wireless and Verizon will merge.
Use Excel’s AVEDEV function to find the mean absolute deviation (MAD) of the integers 1 through 10.
The number of internet users in Latin America grew from 77.2 million in 2009 to 139.1 million in 2016. Use the geometric mean to find the annual growth rate.
From the display below, pick five cards (without replacement) by using random numbers. Explain your method. Why would the other sampling methods not work well in this case? A A Kк 10 10 10 10 9. 8.
Write an Excel formula to generate a random normal deviate from N(4000, 200) and copy the formula into 100 cells.
The length of a time-out during a televised professional football game is normally distributed with a mean of 84 seconds and a standard deviation of 10 seconds. If the network runs consecutive
Why might the following not be normally distributed?(a) The time it takes you to drive to the airport.(b) The annual income for a randomly chosen Major League Baseball player.(c) The annual hurricane
The shoplifting sensor at a certain Best Buy exit gives an alarm 0.5 times a minute.(a) Find the median waiting time until the next alarm.(b) Find the first quartile of waiting time before the next
The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.35 defects per vehicle. Suppose that we inspect 100 Volkswagen vehicles at random.(a) What is the approximate normal
A ski resort pays its part-time seasonal employees on an hourly basis. At a certain mountain, the hourly rates have a normal distribution with σ = $3.00. If 20 percent of all part-time seasonal
Suppose the volume of liquid soap (X) in a randomly chosen bottle of dish soap is normally distributed with μ = 600 ml and σ = 5 ml. Write the Excel function to find the volume associated with the
Suppose X ~ N(56, 4). Write the Excel function to find the X values associated with the following percentages:a. Highest 20 percentb. Middle 60 percentc. Lowest 30 percent
Suppose the volume of liquid soap (X) in a randomly chosen bottle of dish soap is normally distributed with μ = 600 ml and σ = 5 ml. Write the Excel function to calculate the following
Suppose X ~ N(56, 4). Write the Excel function to calculate the following probabilities:a. P(X < 52.3)b. P(X ≥ 58.0)c. P(50.0 ≤ X < 63.7)
If all normal distributions have the same shape, how do they differ?
Jill’s resting heart rate (bpm) is a uniformly distributed random variable ranging between 74 and 77 bpm.(a) What is her average resting heart rate?(b) The standard deviation?(c) What is the
The actual arrival time of the scheduled 10:20 a.m. bus at the Alpine and Broadway stop is a uniformly distributed random variable ranging from 10:18 to 10:23.(a) What is the average arrival time of
For a continuous uniform distribution, why is P(25 < X < 45) the same as P(25 ≤ X ≤ 45)?
Jane is planning to offer a Groupon for inner tube rentals that she will distribute on hot, sunny, summer days by the river that runs through her town. Based on her past experience with Groupon, she

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