Deck 9: Inferences From Two Samples

Question 1

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from
Normally distributed populations. Do not assume that the population standard deviations are
Equal. A paint manufacturer wished to compare the drying times of two different types of
Paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were
Selected and applied to similar surfaces. The drying times, in hours, were recorded. The
Summary statistics are as follows.

Answer 1

D

Question 2

Answer 2

D

Question 3

Answer 3

B

Question 4

Find . The differences between two sets of dependent data are 0.4, 0.24, 0.22, 0.26, 0.34. Round to the nearest hundredth.

A) 0.08
B) 0.12
C) 0.04
D) 0.24

Question 5

Question 6

Question 7

Express the alternative hypothesis in symbolic form. of time (in hours)sophomores spent studying for the statistics final exam is more than that of
Freshmen. Assume that the two samples are independent. Let the freshmen be the first
Population and the sophomores be the second population.

Question 8

Which distribution is used to test the claim that the standard deviation of the ages (in years)of when girls first learn to ride a bike is equal to the standard deviation of the ages (in years)
When boys first lean to ride a bike?

A) Normal
B) t
C) chi-square
D) F

Question 9

Determine whether the samples are independent or dependent. The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug
Treatment. The data consist of before and after intensities for each patient.

A) Independent samples
B) Dependent samples

Question 10

Determine whether the following statement regarding the hypothesis test for two population
proportions is true or false:
However small the difference between two population proportions, for sufficiently large
sample sizes, the null hypothesis of equal population proportions is likely to be rejected.

Question 11

Question 12

Question 13

Question 14

Question 15

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.
Which distribution is used to test the claim that women have a higher mean resting heart rate
Than men?

A) Normal
B) t
C) chi-square
D) F

Question 16

Question 17

Question 18

Find sd. Consider the set of differences between two dependent sets: 84, 85, 83, 63, 61, 100, 98. Round to the nearest tenth.

A) 15.3
B) 16.2
C) 15.7
D) 13.1

Question 19

Question 20

Question 21

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence
Interval for the mean difference between the before and after scores.

Question 22

Question 23

Construct a confidence interval for μd , paired data. Assume that the population of paired differences is normally distributed. Using
The sample paired data below, construct a 90% confidence interval for the population mean
Of all differences.

Question 24

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint)and 9 cans of type B (the
Modified paint)were selected and applied to similar surfaces. The drying times, in hours, were
Recorded. The summary statistics are as follows. What does the confidence interval suggest about the population means?

A) The confidence interval includes only positive values which suggests that the two population means might be equal. There doesn't appear to be a significant difference
Between the mean drying time for paint type A and the mean drying time for paint type B.
The modification does not seem to be effective in reducing drying times.
B) The confidence interval includes 0 which suggests that the two population means might be equal. There doesn't appear to be a significant difference between the mean drying time for
Paint type A and the mean drying time for paint type B. The modification does not seem to
Be effective in reducing drying times.
C) The confidence interval includes only positive values which suggests that the mean drying time for paint type A is smaller than the mean drying time for paint type B. The
Modification does not seem to be effective in reducing drying times.
D) The confidence interval includes only positive values which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The
Modification seems to be effective in reducing drying times.

Question 25

Question 26

Express the alternative hypothesis in symbolic form. An automobile technician claims that the mean amount of time (in hours)per domestic car repair is more than that of foreign cars.
Assume that two samples are independent. Let the domestic car repair times be the first
Population and the foreign car repair times be the second population.

Question 27

Question 28

Question 29

Find the number of successes x suggested by the given statement. A computer manufacturer randomly selects 2680 of its computers for quality assurance and finds that 1.98% of these
Computers are found to be defective.

A) 56
B) 51
C) 58
D) 53

Question 30

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.
Which distribution is used to test the claim that mothers spend more time (in minutes)
Driving their kids to activities than fathers do?

A) Normal
B) t
C) chi-square
D) F

Question 31

Question 32

Question 33

Question 34

Determine whether the samples are dependent or independent. The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and
After drug treatment. The data consist of before and after intensities for each patient.

A) Dependent samples
B) Independent samples

Question 35

Question 36

Question 37

Determine whether the samples are dependent or independent. The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured
For patients who use the medicine and another group of patients who use a placebo drug.

A) Dependent samples
B) Independent samples

Question 38

Which distribution is used to test the claim that the standard deviation of the lengths (in cm)18)___________ of male babies at birth is equal to the standard deviation of the lengths (in cm)of female
Babies at birth?

A) Normal
B) t
C) chi-square
D) F

Question 39

Question 40

Question 41

Suppose you wish to test a claim about the mean of the differences from dependent samples or
to construct a confidence interval estimate of the mean of the differences from dependent
samples. What are the requirements?

Question 42

Identify the test statistic that should be used for testing the following given claims.
a. The mean of the differences between IQ scores of brothers and IQ scores of their sisters is
equal to 0.
b. The proportion of offices with windows is equal to the proportion of offices without
windows.
c. The variation among temperature inside buildings in winter is equal to the variation in the
temperature inside building in summer.
d. The mean age of female math professors is equal to the mean age of male math professors.

Question 43

Test the given claim about the means of two populations. Assume that two dependent samples
have been randomly selected from normally distributed populations. A coach uses a new
technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores
were recorded before and after the training. The results are shown below. Using a 0.01 level of significance, test the claim that the training technique is effective in raising
the gymnasts' scores. Include your null and alternative hypotheses, the test statistic, P-value or
critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your
answer.

Question 44

Question 45

Assume
marketing survey involves product recognition in New York and California. Of 558 New
Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product.
At the 0.05 significance level, test the claim that the recognition rates are the same in both
states. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s),
conclusion about the null hypothesis, and conclusion about the claim in your answer.

Question 46

Assume that the two samples are independent simple random samples selected from normally
distributed populations. Do not assume that the population standard deviations are equal. A
researcher wishes to determine whether people can reduce their resting heart rate by following
a particular diet. Construct a 95% confidence interval estimate for the following data. Does
the confidence interval support that the mean resting heart rate for those on the diet is lower
than that of those not on the diet? Explain your reasoning.

Question 47

Test the indicated claim about the variances or standard deviations of two populations.
that both samples are independent simple random samples from populations having normal
distributions. When 25 randomly selected customers enter any one of several waiting lines,
their waiting times have a standard deviation of 5.35 minutes. When 16 randomly selected
customers enter a single main waiting line, their waiting times have a standard deviation of 2.2
minutes. Use a 0.05 significance level to test the claim that there is more variation in the
waiting times when several lines are used. Include your null and alternative hypotheses, the
test statistic, P-value or critical value(s), conclusion about the null hypothesis, and conclusion
about the claim in your answer.

Question 48

A researcher wishes to determine whether the blood pressure of vegetarians is, on average,
lower than the blood pressure of nonvegetarians. Independent simple random samples of 85
vegetarians and 75 nonvegetarians yielded the following sample statistics for systolic blood
pressure: Use a significance level of 0.01 to test the claim that the mean systolic blood pressure of
vegetarians is lower than the mean systolic blood pressure of nonvegetarians. Include your null
and alternative hypotheses, the test statistic, P-value or critical value(s), conclusion about the
null hypothesis, and conclusion about the claim in your answer.

Question 49

Test the given claim about the means of two populations. Assume that two dependent samples
have been randomly selected from normally distributed populations. A test of abstract reasoning
is given to a random sample of students before and after they completed a formal logic course.
The results are given below. At the 0.05 significance level, test the claim that the mean score is
not affected by the course. Include your null and alternative hypotheses, the test statistic, P-value
or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your
answer.

Question 50

Test the indicated claim about the variances or standard deviations of two populations?
Assume that both samples are independent simple random samples from populations having
normal distributions. A random sample of 16 women resulted in blood pressure levels with a
standard deviation of 23 mm Hg. A random sample of 17 men resulted in blood pressure
levels with a standard deviation of 19.2 mm Hg. Use a 0.05 significance level to test the claim
that blood pressure levels for women vary more than blood pressure levels for men. Include
your null and alternative hypotheses, the test statistic, P-value or critical value(s), conclusion
about the null hypothesis, and conclusion about the claim in your answer.

Question 51

Question 52

A Dean of Students conducted a survey to test the claim that women spend more time visiting
the STEM lab than men do. A survey was administered to a simple random sample of 15
female student volunteers and 12 male volunteers that asked, "How many minutes have you
spent in the STEM lab this semester?" The results are shown below. Test the claim at the 1% level of significance. Assume that the number of minutes that
women and men spent in the STEM lab is normally distributed. Do not assume that the
population standard deviations are equal. Include your null and alternative hypotheses, the
test statistic, P-value or critical value(s), conclusion about the null hypothesis, and conclusion
about the claim in your answer.

Question 53

Test the indicated claim about the means of two populations. Assume that the two samples are
independent simple random samples selected from normally distributed populations. Do not
assume that the population standard deviations are equal. A researcher wishes to determine
whether people with high blood pressure can reduce their blood pressure, measured in mm Hg,
by following a particular diet. Use a significance level of 0.01 to test the claim that the treatment
group is from a population with a smaller mean than the control group. Include your null and
alternative hypotheses, the test statistic, P-value or critical value(s), conclusion about the null
hypothesis, and conclusion about the claim in your answer.

Question 54

Test the given claim about the means of two populations. Assume that two dependent samples
have been randomly selected from normally distributed populations. Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math
scores. Include your null and alternative hypotheses, the test statistic, P-value or critical
value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.

Question 55

Test the indicated claim about the means of two populations. Assume that the two samples are
independent simple random samples selected from normally distributed populations. Do not
assume that the population standard deviations are equal. Use a 0.10 significance level to test the claim that the mean GPA of students at college A is
different from the mean GPA of students at college B. Include your null and alternative
hypotheses, the test statistic, p-value or critical value(s), conclusion about the null hypothesis,
and conclusion about the claim in your answer.

Question 56

Test the indicated claim about the means of two populations. Assume that the two samples are
independent simple random samples selected from normally distributed populations. Do not
assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean amount of time spent watching
television by women is smaller than the mean amount of time spent watching television by
men. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s),
conclusion about the null hypothesis, and conclusion about the claim in your answer.

Question 57

When testing for a difference between the means of a treatment group and a placebo group, the
computer display below is obtained. Using a 0.05 significance level, is there sufficient evidence
to support the claim that the treatment group (variable 1)comes from a population with a mean
that is less than the mean for the placebo population? Explain.

Question 58

To test the null hypothesis that the difference between two population proportions is
equal to a nonzero constant c, use the test statistic

Question 59

Question 60

A researcher wishes to compare how students at two different schools perform on a math test?
He randomly selects 40 students from each school and obtains their test scores. He pairs the
first score from school A with the first school from school B, the second score from school A
with the second school from school B and so on. He then performs a hypothesis test for
matched pairs. Is this approach valid? Why or why not? If it is not valid, how should the
researcher have proceeded?