Deck 11: Inferences for Population Standard Deviations

Question 1

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.
The standard deviation of math test scores at one high school is 16.1. The standard
deviation of the math scores of a random sample of 22 girls was 12. Use a significance level
of 0.01 to test whether the standard deviation, Ϭ, of the girls' test scores is smaller than
16.1. Use the critical-value approach.

Answer 1

Question 2

Decide whether applying one-standard-deviation chi-square procedures to the given data appears reasonable. Explainyour answer.
Test scores for a random sample of 12 students were as follows:

Answer 2

A normal probability plot of the data is given below. Yes, it appears reasonable to apply one-standard-deviation chi-square procedures
to the given data; the normal probability plot is close to linear, indicating that the
variable under consideration is close to being normally distributed. Furthermore,
there are no outliers.

Question 3

Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
A researcher obtained independent random samples of men from two different towns. She
recorded the weights of the men. The results are summarized below: Do the data provide sufficient evidence to conclude that there is more variation in weights
of men from town A than in weights of men from town B? Perform an F-test at the 1%
significance level.

Answer 3

Question 4

Provide an appropriate response.

Question 5

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.

Question 6

Decide whether applying one-standard-deviation chi-square procedures to the given data appears reasonable. Explainyour answer.
The masses, in grams, of 19 plants of a certain type are given below.

Question 7

Provide an appropriate response.
A machine dispenses a liquid drug into bottles in such a way that the standard deviation of
the volumes dispensed is 81 microliters. A new machine is tested on a sample of 24
containers and the standard deviation for this sample group is found to be 50 microliters.
Why would it be important to perform a hypothesis test to determine whether the standard
deviation, Ϭ, of the volumes dispensed by the new machine is less than 81 microliters?

Question 8

Provide an appropriate response.

Question 9

Provide an appropriate response.

Question 10

Decide whether applying one-standard-deviation chi-square procedures to the given data appears reasonable. Explainyour answer.
A machine that fills soda bottles is supposed to fill them to a mean volume of 16.2 fluid
ounces. A random sample of 20 filled bottles produced the following volumes in fluid
ounces:

Question 11

Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
A random sample of 16 women resulted in blood pressure levels with a standard deviation
of 21.7 mm Hg. A random sample of 17 men resulted in blood pressure levels with a
standard deviation of 19 mm Hg. Do the data provide sufficient evidence to conclude that
there is more variation among blood pressure levels for women than among blood
pressure levels for men? Use a 0.025 significance level .

Question 12

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.
A manufacturer uses a new production method to produce steel rods. Under the old
production method, the standard deviation of the lengths of the rods was 3.5 cm. The
standard deviation of the lengths of a random sample of 17 steel rods produced under the
new method was 2.4 cm. At the 0.10 significance level, test whether the standard deviation
of the lengths of the new rods is different from 3.5 cm. Use the critical-value approach.

Question 13

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.
Systolic blood pressure levels for men have a standard deviation of 19.7 mm Hg. A random
sample of 31 women resulted in systolic blood pressure levels with a standard deviation of
22.1 mm Hg. Use a 0.05 significance level to test whether the standard deviation of systolic
blood pressure levels for women is different from 19.7 mm Hg. Use the critical-value
approach.

Question 14

Decide whether applying one-standard-deviation chi-square procedures to the given data appears reasonable. Explainyour answer.
The masses, in grams, of 19 plants of a certain type are given below.

Question 15

Decide whether applying one-standard-deviation chi-square procedures to the given data appears reasonable. Explainyour answer.
Test scores for a random sample of 12 students were as follows:

Question 16

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.
With individual lines at the checkouts, a store manager finds that the standard deviation
for the waiting times on Monday mornings is 5.2 minutes. After switching to a single
waiting line, he finds that for a random sample of 29 customers, the waiting times have a
standard deviation of 4.6 minutes. Use a 0.025 significance level to test whether the
standard deviation of the waiting times using a single line is less than 5.2 minutes. Use the
critical-value approach.

Question 17

Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
A researcher is interested in comparing the amount of variation in women's scores on a
certain test with the amount of variation in men's scores on the same test. Random samples
of 11 men and 13 women yielded the following scores: Do the data provide sufficient evidence to conclude that there is less variation in men's
scores than in women's scores? Perform an F-test at the 5% significance level. (Note:

Question 18

Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
Test scores for random samples of students from two different schools were recorded. The
summary statistics are given below. Do the data provide sufficient evidence to conclude that variation in test scores differs
between students from school A and students from school B? Use a significance level of
0.10.

Question 19

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.
In one town, monthly incomes for men with college degrees are found to have a standard
deviation of $650. A random sample of 22 men without college degrees resulted in
incomes with a standard deviation of $905. At the 1% level of significance, do the data
provide sufficient evidence to conclude that the standard deviation, Ϭ, of incomes of men
in that town without college degrees is greater than $650? Use the critical-value approach.

Question 20

Decide whether applying one-standard-deviation chi-square procedures to the given data appears reasonable. Explainyour answer.
Lifetimes (in hours)for a random sample of 12 batteries are as follows:

Question 21

Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
When 25 randomly selected customers enter any one of several waiting lines, their waiting
times have a standard deviation of 5.21 minutes. When 17 randomly selected customers
enter a single main waiting line, their waiting times have a standard deviation of 2.35
minutes. Do the data provide sufficient evidence to conclude that there is more variation
in the waiting times when several lines are used? Perform an F-test at the 1% significance
level.

Question 22

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.

Question 23

Use the one-standard-deviation chi-square interval procedure to obtain the specified confidence interval for thepopulation standard deviation . Assume that the population has a normal distribution.
The daily intakes of milk (in ounces)for ten five-year old children selected at random from one school were:

Question 24

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).

Question 25

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.
When 12 bolts are tested for hardness, their indexes have a standard deviation of 41.7. Test
the claim that the standard deviation of the hardness indexes for all such bolts is greater
than 30.0. Use a 0.025 level of significance. Use the critical-value approach.

Question 26

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.
A machine dispenses a liquid drug into bottles in such a way that the standard deviation of
the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the
standard deviation for this sample group is found to be 26 milliliters. At the 5% level of
significance, do the data provide sufficient evidence to conclude that the standard
deviation, of the amounts dispensed by the new machine is less than 81 milliliters? Use
the critical-value approach.

Question 27

Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
The manager of a juice bottling factory is considering installing a new juice bottling
machine which she hopes will reduce the amount of variation in the volumes of juice
dispensed into 8-fluid-ounce bottles. Random samples of 9 bottles filled by the new
machine and 10 bottles filled by the old machine yielded the following volumes of juice (in
fluid ounces).

Question 28

A sample standard deviation and sample size are given. Use the one-standard-deviation interval procedure to obtainthe specified confidence interval.

Question 29

Provide an appropriate response.
When you invest your money in a savings account, the standard deviation of the annual
return is small. When you invest your money in the stock market, the standard deviation
of your annual return can be high. In which of the situations below would knowledge of
the standard deviation be more important? Explain your thinking.
A: A 25-year old man will invest money in a mutual fund and plans to leave his money
there for a long period.
B: A 63-year old man nearing retirement will invest money in a mutual fund. He will only
be able to invest for a short period and will then need to withdraw his money.

Question 30

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.

Question 31

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.

Question 32

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).
An F-curve has df = (9, 12). Find the F-value having area 0.005 to its left.

A)0.161
B)6.23
C)0.192
D)5.20

Question 33

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.

Question 34

Use the two-standard-deviations F-interval procedure to find the required confidence interval. Assume that independentsamples have been randomly selected from the two populations and that the variable under consideration is normallydistributed on both populations.

Question 35

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).

Question 36

Provide an appropriate response.

Question 37

Use the one-standard-deviation chi-square interval procedure to obtain the specified confidence interval for thepopulation standard deviation Ϭ. Assume that the population has a normal distribution.

Question 38

Question 39

Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.

Question 40

Question 41

Use the one-standard-deviation chi-square interval procedure to obtain the specified confidence interval for thepopulation standard deviation Ϭ. Assume that the population has a normal distribution.
The mean systolic blood pressure for a random sample of 28 women aged 18-24 is 114.8 mm Hg and the standard deviation is 12.6 mm Hg. Construct a 90% confidence interval for the standard
Deviation Ϭ, of the systolic blood pressures of all women aged 18-24.

Question 42

Provide an appropriate response.
True or false? An F-curve is right-skewed if the numerator degrees of freedom are larger than the
denominator degrees of freedom and left-skewed if the denominator degrees of freedom are larger
than the numerator degrees of freedom.

Question 43

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).

Question 44

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).
An F-curve has df = (60, 10). Find the F-value having area 0.025 to its left.

A)3.20
B)0.441
C)2.27
D)0.313

Question 45

A sample standard deviation and sample size are given. Use the one-standard-deviation x²-test to conduct the requiredhypothesis test.

Question 46

Use the one-standard-deviation chi-square interval procedure to obtain the specified confidence interval for thepopulation standard deviation Ϭ. Assume that the population has a normal distribution.
A football coach randomly selected ten players from his college and timed how long each player took to perform a certain drill. The times (in minutes)were:

Question 47

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-interval procedure to obtain the specified confidence interval. Round tothe nearest hundredth.

Question 48

Provide an appropriate response.

Question 49

Provide an appropriate response.

Question 50

Use the two-standard-deviations F-interval procedure to find the required confidence interval. Assume that independentsamples have been randomly selected from the two populations and that the variable under consideration is normallydistributed on both populations.
A researcher obtained independent random samples of men from two different towns. She recorded the weights of the men. The results are summarized below:

Question 51

Question 52

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).
An F-curve has df = (3, 5). Find the F-value having area 0.01 to its right.

A)3.62
B)0.035
C)12.06
D)28.24

Question 53

Question 54

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).

Question 55

Provide an appropriate response.

Question 56

Question 57

Provide an appropriate response.
True or False? The test for one population standard deviation is robust to moderate violations
of the normality assumption.

Question 58

Provide an appropriate response.

Question 59

Question 60

Question 61

Provide an appropriate response.

Question 62

Provide an appropriate response.

Question 63

A sample standard deviation and sample size are given. Use the one-standard-deviation -test to conduct the requiredhypothesis test.

Question 64

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-interval procedure to obtain the specified confidence interval. Round tothe nearest hundredth.

Question 65

Question 66

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).

Question 67

Question 68

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.

Question 69

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).
An F-curve has df = (6, 24). Find the F-value having area 0.01 to its left.

A)0.272
B)0.137
C)7.31
D)3.67

Question 70

Question 71

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).
An F-curve has df = (24, 3). Find the F-value having area 0.005 to its right.

A)42.62
B)0.181
C)5.52
D)8.64

Question 72

Question 73

Provide an appropriate response.

Question 74

Use the one-standard-deviation chi-square interval procedure to obtain the specified confidence interval for thepopulation standard deviation Ϭ. Assume that the population has a normal distribution.
A sociologist develops a test to assess attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct a 95% confidence interval for the standard deviation, Ϭ, of the scores of all subjects.

A)17.5 to 27.8
B)16.9 to 29.3
C)16.6 to 28.6
D)17.2 to 27.2

Question 75

Provide an appropriate response.

Question 76

Use the F-table and the reciprocal property of F-curves, if necessary, to find the required F-value(s).
An F-curve has df = (15, 10). Find the F-value having area 0.05 to its left.

A)2.54
B)0.394
C)0.351
D)2.85

Question 77

A sample standard deviation and sample size are given. Use the one-standard-deviation -interval procedure to obtainthe specified confidence interval.
s = 6, n = 18 , 99% confidence interval

A)4.139 to 10.365
B)4.28 to 9.773
C)0.693 to 4.342
D)1.69 to 4.231

Question 78

s = 4, n = 11 , 95% confidence interval

A)2.956 to 6.373
B)2.795 to 7.02
C)0.618 to 3.896
D)2.795 to 3.51

Question 79

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.

Question 80

Use the two-standard-deviations F-interval procedure to find the required confidence interval. Assume that independentsamples have been randomly selected from the two populations and that the variable under consideration is normallydistributed on both populations.
A researcher is interested in comparing the amount of variation in women's scores on a certain test and the amount of variation in men's scores on the same test. Independent random samples of 11
Men and 13 women yielded the following scores.