Business 23377 | Course Paper

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In most processes, the process control limits are set to correspond with the specification

limits on the product.

Six food critics each visited and rated four different restaurants. Each critic visited each

restaurant on three separate occasions and recorded a score for each visit. Assume that

results show that there is an interaction. This would mean that, for example, which

restaurant is rated the highest depends on which critic does the rating.

In simple linear regression, the t-test for the slope and the F-test are both conducting the

same hypothesis test.

The Hawkins Company randomly samples 10 items from every large batch before the

batch is packaged and shipped. According to the contract specifications, 5 percent of the

items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of

10, they ship the batch without further inspection. If they find 2 or more, the entire

batch is inspected. Based on this sampling plan, the probability that a batch that meets

the contract requirements will end up being 100 percent inspected is approximately .

0746.

The primary difference between the binomial distribution and the Poisson distribution is

that the Poisson is used to describe a continuous random variable and the binomial is

used for discrete random variables.

The Nationwide Motel Company has determined that 70 percent of all calls for motel

reservations request nonsmoking rooms. Recently, the customer service manager for the

company randomly selected 25 calls. Assuming that the distribution of calls requesting

nonsmoking rooms is described by a binomial distribution, the probability that more

than 20 customers in the sample will request nonsmoking rooms is approximately 0.09.

One of the differences between a stem and leaf diagram and a histogram is that even for

variables involving a large number of different values, the stem and leaf diagram shows

the individual data values whereas the histogram requires you to group the data and lose

the individual values.

A car salesman states that the probability that the dealership sells a car on a Saturday

morning is .30. The method of probability assessment that he has used is most likely

classical assessment.

A perfect correlation between two variables will always produce a correlation

coefficient of +1.0

It is very unlikely that a nonstatistical sample will ever provide less sampling error than

a statistical sample of the same size.

If the correlation between the dependent variable and the independent variable is

negative, the standard error of the regression slope coefficient in a simple linear

regression model will also be negative.

The bottlers of a new fruit juice daily select a random sample of 12 bottles of the drink

to estimate the mean quantity of juice in the bottles filled that day. On one such day, the

following results were observed: = 12.03; s = 0.12. Based on this information, the

margin of error associated with a 90 percent confidence interval estimate for the

population mean is 1.7959 ounces.

In a two-factor ANOVA with replication in which all hypotheses are to be tested using

an alpha = .05 level, if the p-value for interaction is .03467, the decision maker should

conclude that no interaction is present.

The Crystal Window Company makes windows at three locations: Reno, Las Vegas,

and Boise. Some windows made by the company contain a visible defect and must be

replaced. Each defect costs the company $45.00. The Reno plant makes 40 percent of

all windows while the Las Vegas and Boise plants split the remaining production

evenly. A recent quality study shows that 8 percent of the Reno windows contain a

defect, 11 percent of the Las Vegas windows contain a defect, while 4 percent of the

windows made in Boise have a defect. Once the windows are made, they are shipped to

a central warehouse where they are commingled and the location where they were made

is lost.

Based on this information, if a defective window is discovered, it was most likely made

by the Las Vegas plant.

One of the most important aspects of quality improvement is the idea of reducing the

variability in a product or service. For instance, a major bank has worked to reduce the

variability in the service time at the drive-through. The managers believe that the

standard deviation in service time should not exceed 30 seconds. To test whether this

goal is being achieved, a random sample of n = 25 cars is selected each week and the

service time for each car is measured. Last week, the mean time was 345 seconds with a

standard deviation equal to 38 seconds. Given this information, if the significance level

is 0.10, the critical value from the chi-square table is about 34.3.

The owners of Hal’s Cookie Company have collected sales data for the past 8 months.

These data are shown as follows:

Using a starting forecast in period 1 of 100, the forecast bias over periods 2-8 is

negative when a single exponential smoothing model is used with a smoothing constant

of 0.20

The credit card balances for customers at State Bank and Trust has a mean equal to

$800 and a standard deviation equal to $60.00. Kevin Smith’s balance is $1,352. Based

on this, his standardized value is 9.20.

The sample mean is a parameter.

If a time series contains substantial irregular movement, the smoothing constant for a

single exponential smoothing model that is close to 1.0 will result in forecasts that are

not as smoothed out as those that would occur if a smaller smoothing constant was

used.

Managers use contingency analysis to determine whether two categorical variables are

independent of each other.

You are given the following data:

Assuming that these data reflect the population of interest, these data can be considered

symmetric.

A recent study involving a sample of 3,000 vehicles in California showed the following

statistics related to the number of miles driven per day: Q1 = 12, Q2 = 45, and Q3 = 56.

Based on these data, if a box and whisker plot is developed, a value of 110 is an outlier.

If one or more of the regression assumptions has been violated this means that the

current regression model is not the best one for this data set, and another model should

be sought.

A company that makes and markets a device that is aimed at helping people quit

smoking claims that at least 70 percent of the people who have used the product have

quit smoking. To test this, a random sample of n = 100 product users was selected. The

critical value for the hypothesis test using a significance level of 0.05 would be

approximately -1.645.

You should not include more than one categorical variable in a multiple regression

because the use of two or more will cause misleading results.

The within sample variation is the dispersion that exists because the sample means for

the various factor levels are not all equal.

A used car lot has 15 cars. Five of these cars were manufactured in the United States

and the others were made in other countries. If one car is purchased at random from this

car lot, the probability that it is a U.S. car is 0.33.

The population of incomes in a particular community is thought to be highly

right-skewed with a mean equal to $36,789 and a standard deviation equal to $2,490.

Based on this, if a sample of size n = 36 is selected, the highest sample mean that we

would expect to see would be approximately $38,034.

There is no hard-and-fast rule regarding the number of classes that must be used when

establishing a frequency distribution for a continuous variable.

The Good-Guys Car Dealership has tracked the number of used cars sold at its

downtown dealership. Consider the following data as representing the population of

cars sold in each of the 8 weeks that the dealership has been open.

The population standard deviation is approximately 2.87 cars.

In conducting one-way analysis of variance, the sample size for each group must be

equal.

A histogram can be used to display a joint frequency distribution between two

quantitative variables.

In an unstructured interview the questions are scripted.

You are given the following data:

Assuming that the data reflect a sample from a larger population, the sample mean is

30.00.

An ogive is a graph of a joint frequency distribution.

Suppose the time it takes for a customer to be served at a fast-food chain business is

thought to be uniformly distributed between 3 and 8 minutes, then the probability that it

will take exactly 5 minutes is 0.20.

A cell phone company believes that 90 percent of their customers are satisfied. They

survey a sample of n = 100 customers and find that 82 say they are satisfied. In

calculating the standard error of the sampling distribution (σp) the proportion to use is

0.82.

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a

discrete random variable with the following probability distribution:

Based on this information, the standard deviation for the number of no-shows is about

0.36 customers.

When graphed, the probability distribution for a discrete random variable looks like a

histogram.

The null and alternate hypotheses must be opposites of each other.

A study has indicated that the sample size necessary to estimate the average electricity

use by residential customers of a large western utility company is 900 customers.

Assuming that the margin of error associated with the estimate will be 30 watts and the

confidence level is stated to be 90 percent, what was the value for the population

standard deviation?

A) 265 watts

B) Approximately 547.1 watts

C) About 490 watts

D) Can’t be determined without knowing the size of the population.

Which of the following in not an out of control signal for an x-bar chart?

A) One or more points outside the control limits

B) Seven or more consecutive points that all fall on the same side of the center line

C) Six or more consecutive points moving in the same direction (an upward or

downward trend)

D) Fourteen points in a row, alternating up and down

The Carter Department Store has data on the sales volume by department for the past

200 days. The data are in an Excel spreadsheet where column A represents the

department name and column B represents the sales for each day in that department. In

order to construct a bar chart that illustrates the difference in total sales by department

for the 200 days, a required step in Excel will be to:

A) determine the total sales by department.

B) use the frequency function to count the number of occurrences by department.

C) group the data into 5 to 20 classes.

D) determine the class widths.

When testing for independence in a contingency table with 3 rows and 4 columns, there

are ________ degrees of freedom.

A) 5

B) 6

C) 7

D) 12

A multiple regression is shown for a data set of yachts where the dependent variable is

the price in thousands of dollars.

Given this information, what is the null hypothesis for testing the overall model?

A) H0 : β0 = β1 = β2 = β3 = β4 = 0

B) H0 : β1 = β2 = β3 = β4 = 0

C) H0 : β1 = 0

D) H0 : β0 = 0

A study was conducted to determine if differences in new textbook prices exist between

on-campus bookstores, off-campus bookstores, and Internet bookstores. To control for

differences in textbook prices that might exist across disciplines, the study randomly

selected 12 textbooks and recorded the price of each of the 12 books at each of the three

retailers. You may assume normality and equal-variance assumptions have been met.

The partially completed ANOVA table based on the study’s findings is shown here:

Based on the study’s findings, was it correct to block for differences in textbooks?

Conduct the appropriate test at the alpha = 0.10 level of significance.

A) Since F = 39.05 > Fα=0.10 = 1.88, reject the null hypothesis. This means that based

on these sample data we can conclude that blocking is effective.

B) Since F = 39.05 > Fα=0.10 = 1.88, do not reject the null hypothesis. This means that

based on these sample data we can conclude that blocking is not effective.

C) Since F = 40.05 > Fα=0.10 = 1.88, reject the null hypothesis. This means that based

on these sample data we can conclude that blocking is effective.

D) Since F = 40.05 > Fα=0.10 = 1.88, do not reject the null hypothesis. This means that

based on these sample data we can conclude that blocking is not effective

After completing sales training for a large company, it is expected that the salesperson

will generate a sale on at least 15 percent of the calls he or she makes. To make sure

that the sales training process is working, a random sample of n = 400 sales calls made

by sales representatives who have completed the training have been selected and the

null hypothesis is to be tested at 0.05 alpha level. Suppose that a sale is made on 36 of

the calls. Based on this information, what is the test statistic for this test?

A) Approximately 0.1417

B) About z = -3.35

C) z = -1.645

D) t = -4.567

The manager for State Bank and Trust has recently examined the credit card account

balances for the customers of her bank and found that 20% have an outstanding balance

at the credit card limit. Suppose the manager randomly selects 15 customers and finds 4

that have balances at the limit. Assume that the properties of the binomial distribution

apply.

What is the probability of finding 4 customers in a sample of 15 who have “maxed out”

their credit cards?

A) 0.1876

B) 0.8358

C) 0.6482

D) 0.3832

A major tire manufacturer wishes to estimate the mean tread life in miles for one of its

tires. It wishes to develop a confidence interval estimate that would have a maximum

sampling error of 500 miles with 90 percent confidence. A pilot sample of n = 50 tires

showed a sample standard deviation equal to 4,000 miles. Based on this information,

the required sample size is:

A) 124.

B) 246.

C) 174.

D) 196.

Three events occur with probabilities P(E1) = 0.35, P(E2) = 0.15, P(E3) = 0.40. If the

event B occurs, the probability becomes P(E1|B) = 0.25, P(B) = 0.30. Compute P(E1 or

B).

A) 0.575

B) 0.075

C) 0.021

D) 0.475

Given the following null and alternative

Test the hypothesis using α = 0.01 assuming that a sample of n = 200 yielded x = 105

items with the desired attribute.

A) Since -2.17 > -2.33, the null hypothesis is not rejected.

B) Since -1.86 > -1.02, the null hypothesis is not rejected.

C) Since -2.17 > -2.33, the null hypothesis is rejected.

D) Since -1.86 > -1.02, the null hypothesis is rejected.

In conjunction with the housing foreclosure crisis of 2009, many economists expressed

increasing concern about the level of credit card debt and efforts of banks to raise

interest rates on these cards. The banks claimed the increases were justified. A Senate

subcommittee decided to determine if the average credit card balance depends on the

type of credit card used. Under consideration are Visa, MasterCard, Discover, and

American Express. The sample sizes to be used for each level are 25, 25, 26, and 23,

respectively.

State the number of degrees of freedom available for determining the within-samples

variation.

A) 93

B) 95

C) 97

D) 98

A test is conducted to compare three different income tax software packages to

determine whether there is any difference in the average time it takes to prepare income

tax returns using the three different software packages. Ten different persons’ income

tax returns are done by each of the three software packages and the time is recorded for

each. The computer results are shown below.

ANOVA

Based on these results and using a 0.05 level of significance which is correct regarding

the primary hypothesis?

A) The three software packages are not all the same because p-value = 1.6E-14 is less

than 0.05.

B) The three software packages are all the same because p-value = 1.6 is greater than

0.05.

C) The three software packages are not all the same because p-value = 2.66E-5 is less

than 0.05.

D) The three software packages are all the same because p-value = 2.66 is greater than

0.05.

For the following hypothesis:

With n = 20, = 71.2, s = 6.9, and α = 0.1, state the conclusion.

A) Because the computed value of t = 0.78 is not greater than 2.1727, reject the null

hypothesis.

B) Because the computed value of t = 0.78 is not greater than 2.1727, do not reject the

null hypothesis.

C) Because the computed value of t = 0.78 is not greater than 1.3277, reject the null

hypothesis.

D) Because the computed value of t = 0.78 is not greater than 1.3277, do not reject the

null hypothesis.

The mean number of errors per page made by a member of the word processing pool

for a large company is thought to be 1.5 with the number of errors distributed according

to a Poisson distribution. If three pages are examined, what is the probability that more

than 3 errors will be observed?

A) 0.6577

B) 0.6969

C) 0.7324

D) 0.7860

A mail-order business prides itself in its ability to fill customers’ orders in six calendar

days or less on the average. Periodically, the operations manager selects a random

sample of customer orders and determines the number of days required to fill the

orders. Based on this sample information, he decides if the desired standard is not being

met. He will assume that the average number of days to fill customers’ orders is six or

less unless the data suggest strongly otherwise. On one occasion where a sample of 40

customers was selected, the average number of days was 6.65, with a sample standard

deviation of 1.5 days. Can the operations manager conclude that his mail-order business

is achieving its goal? Use a significance level of 0.025 to answer this question.

A) Since 2.2216 < 2.4511, reject H0 and conclude that the mail-order business is not

achieving its goal

B) Since 2.7406 > 2.023, reject H0 and conclude that the mail-order business is not

achieving its goal.

C) Since 2.4421 > 2.023, reject H0 and conclude that the mail-order business is not

achieving its goal.

D) Since 2.2346 < 2.5113, reject H0 and conclude that the mail-order business is not

achieving its goal.

Which of the following describes a treatment in a randomized complete block analysis

of variance?

A) A treatment is a combination of one level of each factor.

B) A treatment is a level associated with each factor of the experiment.

C) A treatment is another term for the data that are collected in the experiment.

D) A treatment is considered to be the analysis that is performed on the sample data.