**Use the given degree of confidence and sample data to construct a
confidence interval for the population mean m.**

**1) **A random sample of 105 light bulbs had a mean life of x-bar
= 438 hours with a standard deviation of s = 39 hours. Construct a 90 percent
confidence interval for the mean life, m, of all light bulbs of this type.

60.1 66.9 70.4 73.2 65.2 64.1

68.5 69.2 64.0 62.4 66.9 71.2

682 61.4 65.7 72.5 74.0 70.0

65.8 69.3 60.4 72.4 58.1 68.3

60.5 66.4 60.5 71.3 67.8 73.2

**MULTIPLE CHOICE. Choose the one alternative that best completes
the statement or answers the question. Assume that a computer was
used to generate the given confidence interval for the population mean,
m. Find the sample mean or margin of error as specified.**

**5)** 33.2 < m < 55.5 Find the
sample mean, x-bar.

a)69.2 < m < 83.2c)74.6 < m < 77.8b)67.7 < m < 84.7d)64.2 < m < 88.2

a)20b)4c)104d)100

**13) **Weights of women in one age group are normally distributed
with a standard deviation s of 12 lb. A researcher wishes to estimate the
mean weight of all women in this age group. Find how large a sample must
be drawn in order to be 90 percent confident that the sample mean will
not differ from the population mean by more than 2.4 lb.

**14) **You wish to estimate the mean weight of machine components
of a certain type and you require a 96% degree of confidence that the sample
mean will be in error by no more than 0.009 g. After using the range rule
of thumb to estimate the standard deviation, find the sample size required.
Typical weights range from 8.20 g to 8.40 g.

Use this expression to determine the sample size needed in the following situation:

You wish to estimate the mean height of a population by sampling without
replacement from the population. The size of the population is N = 180.
You wish to be 96% confident that the sample mean is within 0.8 inches
of the true mean. Assume that s = 3.6 inches.
**a) **47 **b) **67
**c) **59 **d) **18

**19) **Of 315 randomly selected medical students, 23 said that
they planned to work in a rural community. Find a 95% confidence interval
for the true proportion of all medical students who plan to work in a rural
community.

**b) **0.0353 < p < 0.111 **d) **0.0443 < p < 0.102

**Identify the null hypothesis H0 and the alternative hypothesis
H1. Use m for a claim about a mean, p for a claim about a proportion, and
s for a claim about variation.**
**21) **An entomologist writes an article in a scientific journal
which claims that fewer than 16 in ten thousand male fireflies are unable
to produce light due to a genetic mutation. Use the parameter p, the true
proportion of fireflies unable to produce light.

**24) **A researcher claims that 62% of voters favor gun control.
Assuming that a hypothesis test of the claim has been conducted and that
the conclusion is failure to reject the null hypothesis, state the conclusion
in nontechnical terms.

a)0.6030b)0.3015c)0.3970d)0.6985

A 129-item sample has a mean x-bar = 34,371. Compute the value of the test statistic.

**28) **A researcher claims that the amounts of acetaminophen
in a certain brand of cold tablets have a mean different from the 600 mg
claimed by the manufacturer. You wish to test this claim at the 0.05 level
of significance. The mean acetaminophen content for a random sample of
n = 44 tablets is 603.8 mg with a standard deviation of 4.6 mg. Compute
the value of the test statistic.

a)Reject H0 if test statistic > 1.96 or < -1.96.b)Reject H0 if test statistic > 1.96.c)Reject H0 if test statistic < 1.645.d)Reject H0 if test statistic > 1.645.

**Solve the problem.**
**30) **In a hypothesis test, the null hypothesis of m = 60
was not rejected because the P-value was greater than 0.05. The sample
size was 65 and the sample mean was 63.5. What can you conclude about the
possible range of values for s, the sample standard deviation?

a)The value of s is greater than 17.15.b)The value of s is greater than 14.43.c)The value of s is less than 14.43.d)The value of s is less than 17.15.

**What decision rule should you use to test the null hypothesis?**

**SHORT ANSWER. Write the word or phrase that best completes each statement
or answers the question. Test the given claim by using the p-value method
of testing hypotheses. Assume that the sample is a simple random sample
selected from a normally distributed population. Include the hypotheses,
the test statistic, the p-value, and your conclusion.**
**32) **Test the claim that the mean lifetime of car engines of
a particular type is greater than 220,000 miles. Sample data are summarized
as n = 23, x-bar = 226,450 miles, and s = 11,500 miles. Use a significance
level of a = 0.01.

**MULTIPLE CHOICE. Choose the one alternative that best completes the
statement or answers the question. Compute the value of an appropriate
test statistic for the given hypothesis test.**
**33) **A cereal company claims that the mean weight of the
cereal in its packets is at least 14 oz. You wish to test this claim at
the 0.02 level of significance. The mean weight for a random sample n =
12 cereal packets is 13.4 ounces with a standard deviation of 0.8 ounces.
Compute the value of the appropriate test statisic.

**a) **-2.921 **b) **±2.947 **c) **-2.583 **d) **-2.602

**SHORT ANSWER. Write the word or phrase that best completes each statement
or answers the question. Test the given claim by using the p-value method
of testing hypotheses. Assume that the sample is a simple random sample
selected from a normally distributed population. Include the hypotheses,
the test statistic, the p-value, and your conclusion.**
**35) **Test the claim that the mean age of the prison population
in one city is less than 26 years. Sample data are summarized as n = 25,
x-bar = 24.4 years, and s = 9.2 years. Use a significance level of a=
0.05.

**38) **In a sample of 162 children selected randomly from
one town, it is found that 32 of them suffer from asthma. At the 0.05 significance
level, test the claim that the proportion of all children in the town who
suffer from asthma is 11%.