Deck 9: Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Question 1

A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this
Particular manufacturer from one day to the next. Twenty-eight random working days were
Selected and each plan was monitored and the number of items produced each day was recorded.
Some of the collected data is shown below: What type of analysis will best allow the manufacturer to determine which plan is more effective?

A)An independent samples comparison of population proportions.
B)A test of a single population proportion.
C)A paired difference comparison of population means.
D)An independent samples comparison of population means.

Answer 1

C

Question 2

Answer 2

C

Question 3

Which of the following represents the difference in two population means?

Answer 3

D

Question 4

Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs
In the low-tech industry with CEOs in the consumer products industry. Using the printout, which of the following assumptions is not necessary for the test to be valid?

A)The population means are equal.
B)The population variances are equal.
C)The samples were randomly and independently selected.
D)Both populations have approximately normal distributions.

Question 5

Question 6

Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs
In the low tech industry with CEOs in the consumer products industry.

Question 7

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female
Purchasers of the product. It was desired to test to determine if the mean age of all female
Purchasers exceeds the mean age of all male purchasers. The sample data is shown here:
Female: n = 10, sample mean = 50.30, sample standard deviation = 13.215
Male: n = 10, sample mean = 39.80, sample standard deviation = 10.040
Which of the following assumptions must be true in order for the pooled test of hypothesis to be
Valid?
I. Both the male and female populations of ages must possess approximately normal probability
Distributions.
II. Both the male and female populations of ages must possess population variances that are
Equal.
III. Both samples of ages must have been randomly and independently selected from their
Respective populations.

A)I only
B)I, II, and III
C)II only
D)III only

Question 8

Question 9

Salary data were collected from CEOs in the consumer products industry and CEOs in the telecommunication industry. The data were analyzed using a software package in order to
Compare mean salaries of CEOs in the two industries. What of the following assumptions is necessary to perform the test described above?

A)The population of salaries for each of the two industries has an approximately normal distribution.
B)The standard deviations of the two populations of salaries are both large.
C)The means of the two populations of salaries are equal.
D)None. The Central Limit Theorem takes care of all assumptions

Question 10

Independent random samples of 100 observations each are chosen from two normal
populations with the following means and standard deviations.

Question 11

In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds
Most comfortable. The data are summarized below: Find the standard error of the estimate for the difference in mean comfortable room temperatures
Between adults and children.

A)1.6279
B)0.7000
C)0.1871
D)0.8367

Question 12

When blood levels are low at an area hospital, a call goes out to local residents to give blood. The blood center is interested in determining which sex - males or females - is more likely to respond.
Random, independent samples of 60 females and 100 males were each asked if they would be
Willing to give blood when called by a local hospital. A success is defined as a person who
Responds to the call and donates blood. The goal is to compare the percentage of the successes
Between the male and female responses. What type of analysis should be used?

A)A test of a single population proportion.
B)An independent samples comparison of population means.
C)An independent samples comparison of population proportions.
D)A paired difference comparison of population means.

Question 13

Consider the following set of salary data: What assumptions are necessary to perform a test for the difference in population means?

A)The two samples were independently selected from the populations of men and women.
B)The population variances of salaries for men and women are equal.
C)Both of the target populations have approximately normal distributions.
D)All of the above are necessary.

Question 14

Which of the following represents the difference in two population proportions?

Question 15

Question 16

Question 17

In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds
Most comfortable. The data are summarized below: Suppose that the psychologist decides to construct a 99% confidence interval for the difference in
Mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99%
Confidence interval turns out to be (-2.9, 3.1). Select the correct statement.

A)It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults.
B)It can be concluded at the 99% confidence level that the true mean comfortable room temperature is between -2.9 and 3.1.
C)It cannot be concluded at the 99% confidence level that there is actually a difference between the true mean comfortable room temperatures for the two groups.
D)It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children.

Question 18

Which of the following represents the ratio of variances?

Question 19

Question 20

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female
Purchasers of the product. What type of analysis should be used to compare the mean age of male
And female purchasers?

A)A paired difference comparison of population means.
B)An independent samples comparison of population means.
C)A test of a single population mean.
D)An independent samples comparison of population proportions.

Question 21

Consider the following set of salary data:

Question 22

In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds
Most comfortable. The data are summarized below:

Question 23

Question 24

Data were collected from CEOs in the consumer products industry and CEOs in the telecommunication industry. The data were analyzed using a software package in order to
Compare mean salaries of CEOs in the two industries.

Question 25

The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful energy at a lower cost. The cost is measured by plant investment per
Delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less the industrial
Plant pays for delivered energy. Suppose we wish to determine if there is a difference in the
Average investment/quad between using electricity and using gas. Our null and alternative
Hypotheses would be:

Question 26

Independent random samples selected from two normal populations produced the
following sample means and standard deviations.

Question 27

Question 28

Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs
In the low-tech industry and CEOs in the consumer products industry.

Question 29

In order to compare the means of two populations, independent random samples of 144
observations are selected from each population with the following results.

Question 30

Consider the following set of salary data:

Question 31

Question 32

Question 33

Data were collected from CEOs in the consumer products industry and the CEOs in the telecommunication industry. The data were analyzed using a software package in order to
Compare mean salaries of CEOs in the two industries.

Question 34

Independent random samples from normal populations produced the results shown
below.

Question 35

Consider the following set of salary data:

Question 36

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female
Purchasers of the product. It was desired to test to determine if the mean age of all female
Purchasers exceeds the mean age of all male purchasers. The sample data is shown here:

Question 37

Question 38

In order to compare the means of two populations, independent random samples of 225
observations are selected from each population with the following results.

Question 39

Question 40

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female
Purchasers of the product. It was desired to test to determine if the mean age of all female
Purchasers exceeds the mean age of all male purchasers. The sample data is shown here:

Question 41

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female
Purchasers of the product. It was desired to test to determine if the mean age of all female
Purchasers exceeds the mean age of all male purchasers. The sample data is shown here:

Question 42

We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each
Brand of cola at each supermarket. The data are shown in the following table: If the problem above represented a paired difference, what assumptions are needed for a
Confidence interval for the mean difference to be valid?

A)The population variances are equal.
B)The population of paired differences has an approximately normal distribution.
C)The samples were independently selected from each population.
D)All of the above are needed.

Question 43

Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items
Common to each of two supermarkets (labeled A and B)and recorded the prices charged by each
Supermarket. The summary results are provided below:

Question 44

Independent random samples selected from two normal populations produced the
following sample means and standard deviations.

Question 45

Question 46

A new weight-reducing technique, consisting of a liquid protein diet, is currently
undergoing tests by the Food and Drug Administration (FDA)before its introduction into
the market. The weights of a random sample of five people are recorded before they are
introduced to the liquid protein diet. The five individuals are then instructed to follow the
liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds)are
again recorded. The results are listed in the table. Let μ1 be the true mean weight of
individuals before starting the diet and let μ2 be the true mean weight of individuals after
3 weeks on the diet. Calculate a 90% confidence interval for the difference between the mean weights before
and after the diet is used.

Question 47

Question 48

Question 49

We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each
Brand of cola at each supermarket. The data are shown in the following table:

Question 50

In order for the results of a paired difference experiment to be unbiased, the experimental units in
each pair must be chosen independently of one another.

Question 51

Using paired differences removes sources of variation that tend to inflate

Question 52

Question 53

Question 54

The data for a random sample of five paired observations are shown below.

Question 55

Question 56

A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine
Types were randomly selected and were tested using each of the two engine oils. The number of
Hours of continuous use before engine breakdown was recorded for each engine oil. Based on the
Information provided, what type of analysis will yield the most useful information?

A)Matched pairs comparison of population proportions.
B)Independent samples comparison of population proportions.
C)Independent samples comparison of population means.
D)Matched pairs comparison of population means.

Question 57

Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items
Common to each of two supermarkets (labeled A and
B)and recorded the prices charged by each supermarket. The summary results are provided below:

Question 58

The data for a random sample of six paired observations are shown below.

Question 59

A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this
Particular manufacturer from one day to the next. Twenty-eight random working days were
Selected and each plan was monitored and the number of items produced each day was recorded.
Some of the collected data is shown below: What assumptions are necessary for the above test to be valid?

A)None of these listed, since the Central Limit Theorem can be applied.
B)The population variances must be approximately equal.
C)Both populations must be approximately normally distributed.
D)The population of paired differences must be approximately normally distributed.

Question 60

An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50
Bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount
Of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to
Determine whether the new spray coating improves the wear of the bicycle tires. The data and
Summary information is shown below:

Question 61

Question 62

An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50
Bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount
Of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to
Determine whether the new spray coating improves the wear of the bicycle tires. The data and
Summary information is shown below:

Question 63

An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50
Bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount
Of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to
Determine whether the new spray coating improves the wear of the bicycle tires. The data and
Summary information is shown below:

Question 64

In an exit poll, 42 of 75 men sampled supported a ballot initiative to raise the local sales tax
to build a new football stadium. In the same poll, 41 of 85 women sampled supported the
initiative. Find and interpret the p-value for the test of hypothesis that the proportions of
men and women who support the initiative are different.

Question 65

Determine whether the sample sizes are large enough to conclude that the sampling
distributions are approximately normal.

Question 66

Question 67

A paired difference experiment produced the following results.

Question 68

Question 69

A cola manufacturer invited consumers to take a blind taste test. Consumers were asked to decide which of two sodas they preferred. The manufacturer was also interested in what factors played a
Role in taste preferences. Below is a printout comparing the taste preferences of men and women.

Question 70

Question 71

One indication of how strong the real estate market is performing is the proportion of
properties that sell in less than 30 days after being listed. Of the condominiums in a
Florida beach community that sold in the first six months of 2006, 75 of the 115 sampled
had been on the market less than 30 days. For the first six months of 2007, 25 of the 85
sampled had been on the market less than 30 days. Test the hypothesis that the proportion
of condominiums that sold within 30 days decreased from 2006 to

Question 72

A government housing agency is comparing home ownership rates among several
immigrant groups. In a sample of 235 families who emigrated to the U.S. from Eastern
Europe five years ago, 165 now own homes. In a sample of 195 families who emigrated to
the U.S. from Pacific islands five years ago, 125 now own homes. Write a 95% confidence
interval for the difference in home ownership rates between the two groups. Based on the
confidence interval, can you conclude that there is a significant difference in home
ownership rates in the two groups of immigrants?

Question 73

Question 74

Question 75

Question 76

Question 77

A paired difference experiment yielded the following results.

Question 78

We sampled 100 men and 100 women and asked: ʺDo you think the environment is a major concern?ʺ Of those sampled, 67 women and 53 men responded that they believed it is. For the
Confidence interval procedure to work properly, what additional assumptions must be satisfied?

A)The population variances are equal.
B)Both samples were randomly and independently selected from their respective populations.
C)Both populations have approximate normal distributions.
D)All of the above are necessary.

Question 79

Question 80

Determine whether the sample sizes are large enough to conclude that the sampling
distributions are approximately normal.