BUS 83068 | Course Paper

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Using either the critical value rule or the p-value rule, if a one-sided null hypothesis is

rejected at a given significance level, then the corresponding two-sided null hypothesis

(i.e., the same sample size, the same standard deviation, and the same mean) will

______________ be rejected at the same significance level.

A. always

B. sometimes

C. never

According to data from the state blood program, 40 percent of all individuals have

group A blood. If six individuals give blood, find the mean number of individuals

having group A blood.

A. 1.2

B. 1.55

C. 1.44

D. 2.4

In which of the following tests is the variable of interest the difference between the

values of the observations from the two samples, rather than the actual observations

themselves?

A. a test of hypothesis about the mean of a population of paired differences selected

from two related samples

B. a test of hypothesis about the difference between the means of two normally

distributed populations using independent samples

C. a test of hypothesis about the difference between two population proportions, using

large independent random samples

D. a test of hypothesis about the difference between the variances of two normally

distributed populations using independent samples

In a major midwestern university, 55 percent of all undergraduates are female, 25

percent of all undergraduates belong to a Greek organization (fraternity or sorority), and

40 percent of all males belong to a Greek organization. What is the probability that an

undergraduate is in a Greek organization, given that the undergraduate is a female?

A. .07

B. .55

C. .127

D. .039

E. 138

If n = 15 and p = .4, then the standard deviation of the binomial distribution is

A. 9.

B. 6.

C. 3.6.

D. 1.897.

E. .4.

Find z when the area to the right of z is .1314.

A. 1.12

B. 0.55

C. −0.55

D. −1.12

In the upcoming election for governor, the most recent poll, based on 900 respondents,

predicts that the incumbent will be reelected with 55 percent of the votes. What is ?

A. .00825

B. .0166

C. .0247

D. .0003

Alternatives 1 and 2 in the following payoff table represent the two possible

manufacturing strategies that the EKA manufacturing company can adopt. The level of

demand affects the success of both strategies. The states of nature (SI) represent the

levels of demand for the company products. S1, S2, and S3 characterize high, medium,

and low demand, with probabilities of .3, .6, and .1, respectively. The payoff values are

in thousands of dollars.

Find the expected monetary value for each of the alternatives and determine the best

alternative (course of action) for the EKA manufacturing company using the expected

monetary value criterion.

A. EMV1 = $98,000, EMV2 = $95,000, choose strategy 1

B. EMV1 = $88,000, EMV2 = $95,000, choose strategy 2

C. EMV1 = $88,000, EMV2 = $85,000, choose strategy 1

D. EMV1 = $66,667, EMV2 = $76,667, choose strategy 2

E. EMV1 = $120,000, EMV2 = $110,000, choose strategy 1

Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3.

Calculate the mean of the distribution.

A. 0.500

B. 0.333

C. 1.500

D. 3.000

A foreman wants to use an chart to control the average length of the bolts

manufactured. He has recently collected the six samples given below.

Sample

1 1.99 2.01 2.02 2.02

2 2.00 2.00 2.01 2.01

3 1.98 1.99 2.01 1.98

4 2.01 2.02 2.02 1.99

5 1.99 1.99 2.01 1.99

6 2.03 1.98 2.03 2.04

Determine the LCL and the UCL for the R chart.

A. [0, .0685]

B. [0, .076]

C. [0, .03]

D. [0, .0601]

A real estate company is analyzing the selling prices of residential homes in a given

community. 140 homes that have been sold in the past month are randomly selected and

their selling prices are recorded. The statistician working on the project has stated that

in order to perform various statistical tests, the data must be distributed according to a

normal distribution. In order to determine whether the selling prices of homes included

in the random sample are normally distributed, the statistician divides the data into 6

classes of equal size and records the number of observations in each class. She then

performs a chi-square goodness-of-fit test for normal distribution. The results are

summarized in the following table.

At a significance level of .05, we

A. reject H0; conclude that the residential home selling prices are not distributed

according to a normal distribution.

B. do not reject H0; conclude that the residential home selling prices are not distributed

according to a normal distribution.

C. reject H0; conclude that the residential home selling prices are distributed according

to a normal distribution.

D. do not reject H0; conclude that the residential home selling prices are distributed

according to a normal distribution.

What sample size is needed to estimate the proportion of highway speeders within 5

percent using a 90 percent confidence level?

A. 385

B. 68

C. 271

D. 165

The Consumer Price Index and the Producer Price Index are both calculated using the

___________ index formula.

A. Paasche

B. weighted aggregate

C. Laspeyres

D. cyclical (seasonal)

A discrete probability distribution is expressed as a table, graph, or ___________ that

gives the probability associated with each possible value that the random variable can

assume.

A. binomial

B. formula

C. Poisson

D. hypergeometric

According to data from the state blood program, 40 percent of all individuals have

group A blood. If six individuals give blood, find the probability that exactly three of

the individuals have group A blood.

A. .4000

B. .2765

C. .5875

D. .0041

Which of the following is a categorical variable?

A. air temperature

B. bank account balance

C. daily sales in a store

D. whether a person has a traffic violation

E. value of company stock

If x is a Poisson random variable with a mean of 10, what is the probability that x is

greater than or equal to 2?

A. .9972

B. .0028

C. .9995

D. .0005

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which

are defective. If one item is drawn from each container, what is the probability that the

item from Container 1 is defective and the item from Container 2 is not defective?

A. 0.3846

B. 0.2250

C. 0.3750

D. 0.6154

E. 0.1500

XYZ Company, Annual Data

Based on the information given in the table above, what is the MSD?

A. 1.3333

B. 1.6667

C. 2.5

D. 3.3333

E. 4.5

An international economist believes that there is a significant relationship between the

amount of debt and the rate of unemployment. He randomly selected six countries to

determine if there is a significant relationship between debt and unemployment rate. In

the following table, debt figures for the 6 countries are given in billions of dollars and

the corresponding unemployment rate is given in percentages. He also discovered that

both the distribution of debt and the distribution of unemployment rate were highly

skewed. Use Spearman’s rank correlation and determine if there is a significant

correlation between debt and unemployment rate. Show the rank correlation.

Country Debt Unemployment Rate

1 1 5

2 3 5

3 5 8

4 1 4

5 6 8

6 6 12

A. rs = .914, reject the null hypothesis.

B. rs = .886, do not reject the null hypothesis.

C. rs = .886, reject the null hypothesis.

D. rs = .914, do not reject the null hypothesis.

In testing the difference between the means of two normally distributed populations

using independent random samples, the correct test statistic to use is the

A. z statistic.

B. t statistic.

C. F statistic.

D. chi-square statistic.

E. None of the other choices is correct.

A manufacturer of cell phone batteries claims that the median life of a battery is more

than 40 hours. Suppose a random sample of 75 batteries finds that 32 have a life of

more than 40 hours. Using α = .05, can we conclude that the battery life is more than 40

hours?

A. Reject the null hypothesis; z = 1.38.

B. Do not reject the null hypothesis; z = 1.38.

C. Reject the null hypothesis; z = −1.38.

D. Do not reject the null hypothesis; z = −1.38.

A normal distribution with mean equal to zero and a standard deviation equal to one is

called the ____________ normal distribution.

A. continuous

B. uniform

C. exponential

D. standard

In a statistics class, 10 scores were randomly selected, with the following results: 74,

73, 77, 77, 71, 68, 65, 77, 67, 66.

What is the 90th percentile?

A. 77

B. 73

C. 74

D. 67

E. 65.9

The chief chemist for a major oil and gasoline production company claims that the

regular unleaded gasoline produced by the company contains on average 4 ounces of a

certain ingredient. The chemist further states that the distribution of this ingredient per

gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2

ounces. What is the probability of finding an average of less than 3.85 ounces of this

ingredient from 64 randomly inspected 1-gallon samples of regular unleaded gasoline?

A. .1587

B. .8413

C. .1357

D. .8643

Suppose the daily change in price of a stock is normally distributed with mean = .20

and standard deviation = .30. What price change is associated with the 25th percentile?

A. .1925

B. .2075

C. .401

D. −.001

A set of final examination grades in a calculus course was found to be normally

distributed with a mean of 69 and a standard deviation of 9. Only 5 percent of the

students taking the test scored higher than what grade?

A. 70.04

B. 67.96

C. 55.48

D. 82.52

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table

below.

At a significance level of .05, which one of the following rejection point conditions is

correct regarding the null hypothesis, H0: D1 and D2 are identical probability

distributions, and the alternative hypothesis of Ha: D1 is shifted to the left of D2

A. Reject H0 if T ≥ 83.

B. Reject H0 if T ≤ 127.

C. Reject H0 if T ≥ 131.

D. Reject H0 if T ≤ 83.

E. Reject H0 if T ≤ 79.

The following is a relative frequency distribution of grades in an introductory statistics

course.

If this was the distribution of 200 students, give the frequency distribution for this data.

The following is a relative frequency distribution of grades in an introductory statistics

course.

If this was the distribution of 200 students, find the frequency for the highest two

grades.

A. 44

B. 118

C. 59

D. 74

E. 35

When using Chebyshev’sTheorem to obtain the bounds for 99.73 percent of the values

in a population, the interval generally will be ___________ the interval obtained for the

same percentage if a normal distribution is assumed (Empirical Rule).

A. shorter than

B. wider than

C. the same as

A company has developed a new ink-jet cartridge for its printer that it believes has a

longer lifetime on average than the one currently being produced. To investigate its

length of life, 240 of the new cartridges were tested by counting the number of

high-quality printed pages each was able to produce. The sample mean and standard

deviation were determined to be 1511.4 pages and 35.7 pages, respectively. The

historical average lifetime for cartridges produced by the current process is 1502.5

pages. At α = .05, test the claim that the new cartridge has a longer lifetime using the

critical value rule.

Based on a random sample of 25 units of product X, the average weight is 102 lb and

the sample standard deviation is 10 lb. We would like to decide whether there is enough

evidence to establish that the average weight for the population of product X is greater

than 100 lb. Assume the population is normally distributed. What is the value of the test

statistic to test the claim?

It has been hypothesized that, on average, employees spend one hour a day playing

video games at work. To test this at her company, a manager takes a random sample of

35 employees, who showed a mean time of 55 minutes per day, with an assumed

population standard deviation of 5 minutes. Calculate the test statistic.

Consider the one-way ANOVA table.

Source df Sum of Squares

Model 3 213.88125

Error 20 11.208333

Total 23 225.0895

What is the mean square error?

Consider a standard deck of 52 playing cards, a randomly selected card from the deck,

and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C =

club.

Are N and C mutually exclusive?

A. Yes, mutually exclusive.

B. No, not mutually exclusive.

Alternatives 1 and 2 in the following payoff table represent the two possible

manufacturing strategies that the EKA manufacturing company can adopt. The level of

demand affects the success of both strategies. The states of nature (SI) represent the

levels of demand for the company products. S1, S2, and S3 characterize high, medium,

and low demand, respectively. The payoff values are in thousands of dollars.

The management believes that weather conditions significantly affect the level of

demand. 48 monthly sales reports are randomly selected. These monthly sales reports

show 15 months with high demand, 28 months with medium demand, and 5 months

with low demand. 12 of the 15 months with high demand had favorable weather

conditions. 14 of the 28 months with medium demand had favorable weather

conditions. Only 1 of the 5 months with low demand had favorable weather conditions.

Based on this information, the prior probabilities have been revised. If the weather

conditions are favorable, P(S1) = .4286, P(S2) = .5357, and P(S3) = .0357; and if the

weather conditions are poor, P(S1) = .1364, P(S2) = .6818, and P(S3) = .1818. It is also

determined that the probability of favorable weather is 0.56 and the probability of poor

weather is 0.44.

Carry out a preposterior analysis and, using the revised probabilities, determine (1) the

expected monetary value when the weather conditions are favorable and (2) the

expected monetary value when the weather conditions are poor.

When testing H0: σ12 ≤ σ22 and HA: σ12> σ22, where s12 = .004, s22 = .002, n1 = 4, and

n2 = 7 at α = .05, what is the decision on H0?

Do not reject the null hypothesis.

Employees of a local university have been classified according to gender and job type.

Are gender and type of job statistically independent?

A. Yes

B. No

ANOVA table

An experiment was performed on a certain metal to determine if the strength is a

function of heating time. The simple linear regression equation is = 1 + 1X. The time

is in minutes and the strength is measured in pounds per square inch. The 95 percent

confidence interval for the slope is from .564 to 1.436. Can we reject β1 = 0?

What is the degrees of freedom treatment (between-group variation) of a completely

randomized design (one-way) ANOVA test with 4 groups and 15 observations per each

group?

A data set with 7 observations yielded the following. Use the simple linear regression

model.

Find the estimated y-intercept.

Consider the following partial analysis of variance table from a randomized block

design with 10 blocks and 6 treatments.

Source SS

Treatments 2,477.53

Blocks 3,180.48

Error 11,661.38

Total

What is the treatment mean square?

A test of mathematical ability is given to a random sample of 10 eighth-grade students

before and after they complete a semester-long basic mathematics course. The mean

score before the course was 119.60, and after the course the mean score was 130.80.

The standard deviation of the difference is 16.061. Calculate a 99 percent confidence

interval.