**Class Examples Confidence Intervals**

1) Compute the
critical value ** ****Z _{α}**

A) 1.96 B) 1.645 C) 1.88 D) 2.33

2) In a sample of 10
randomly selected women, it was found that their mean height was 63.4 inches.
From previous studies, it is assumed that the standard deviation,** ****s**** =**
2.4. Construct the 95% confidence interval for the population mean.

A) (60.8, 65.4) B)
(58.1, 67.3) C) (61.9, 64.9) D) (59.7, 66.5)

3) A random sample
of 40 students has a mean annual earnings of $3120 and
a population standard deviation of $677. Construct the confidence interval for
the population mean, if α
= 0.05.

A) ($1987, $2346) B) ($210, $110) C)
($2910,
$3330)
D) ($4812, $5342)

4) A group of 49
randomly selected students has a mean age of 22.4 years with a population
standard deviation of 3.8. Construct a 98% confidence interval for the
population mean.

A) (19.8, 25.1) B) (21.1, 23.7) C)
(18.8,
26.3) D) (20.3, 24.5)

5) In a random
sample of 60 computers, the mean repair cost was $150 with a population
standard deviation of $36. Construct a 99% confidence interval for the
population mean.

A) ($138, $162)
B) ($238, $274) C) ($537, $654) D) ($18, $54)

6) In a recent study
of 42 eighth graders, the mean number of hours per week that they watched
television was 19.6 with a population standard deviation of 5.8 hours. Find the
98% confidence interval for the population mean.

A) (17.5, 21.7) B) (18.3,
20.9) C) (14.1, 23.2) D) (19.1, 20.4)

7) A 90% confidence
interval for the mean percentage of airline reservations being canceled on the
day of the flight is (3.2 %, 7 %). What is the point estimator of the mean
percentage of reservations that are canceled on the day of the flight?

A) 3.50% B) 1.90% C) 3.8% D) 5.10%

8) Suppose a 90% confidence
interval for
**
μ**
turns out to be ( 110, 260). Based on
the interval, do you believe the average is equal to 270?

A) Yes, and I am 100% sure of it. B) Yes, and I am 90% sure of it.
C)
No, and I am 90%
sure of it. D) No, and
I am 100% sure of it.

9) A random sample of 120 students has a test score average with a standard deviation of 9.1.

Find the margin of error if α = 0.10

A)
0.12 B) 0.83 C) 0.75 D) 1.37

10) A nurse at a
local hospital is interested in estimating the birth weight of infants. How
large a sample must she select if she desires to be 90% confident that the true mean is
within 4 ounces of the sample mean? The
standard deviation of the birth weights is known to be 6 ounces.

11) The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed below.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

What is the effect on the width of the confidence interval
if the sample size is increased to 20?

A) The width decreases. B) It is
impossible to tell without more information.

C) The width remains the same. D) The width increases.

12) B = 3, s^{2} = 60, (1 -
α) = .95. ** ** Find the sample size needed to estimate
**μ.**

A) 77 B) 26 C) 19 D) 1537

13) Suppose a 98 % confidence
interval for
**μ ** turns out to be (1000, 2100). If this
interval was based on a sample of size n =
19 explain what assumptions are necessary for this interval to be valid.

A) The sampling distribution must be biased with 18 degrees of freedom.

B) The sampling distribution of the sample mean must have a
normal distribution.

C) The population must have an approximately normal
distribution.

D) The population of salaries must have an approximate t
distribution.

14)
The principal at Lakewood Elementary would like to estimate the mean length of
time each day that it takes all the buses to arrive and
unload the students. How large a sample is needed if the principal would like
to assert with 90% confidence that the sample mean is off by, at most, 7
minutes. Assume s = 14 minutes.

15) Find the
critical t-value that corresponds to
α = 0.01 and n = 10.

A) 2.262 B) 1.833 C) 2.2821 D) 3.250

16) Find the
critical t-value that corresponds to
α = 0.10 and n = 15.

A) 2.145 B) 1.345 C)
2.624 D) 1.761

17) Construct a 95%
confidence interval for the population mean,
**μ**. Assume the population has a normal
distribution. A sample of 20 college students had mean annual earnings of $3120
with a standard deviation of $677.

A)
($2135, $2567) B) ($2657, $2891) C)
($2803,
$3437) D) ($1324, $1567)

18) Construct a 95%
confidence interval for the population mean,
**μ**. Assume the population has a normal
distribution. A sample of 25 randomly selected students has a mean test score
of 81.5 with a standard deviation of 10.2.

A) (87.12, 98.32) B) (66.35,
69.89)
C) (77.29, 85.71) D) (56.12,
78.34)

19) Construct a 99%
confidence interval for the population mean,
**μ**. Assume the population has a normal
distribution. A group of 19 randomly selected students has a mean age of 22.4
years with a standard deviation of 3.8 years.

A) (18.7, 24.1) B) (19.9, 24.9) C) (16.3, 26.9) D) (17.2, 23.6)

20) A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed.

$3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00

Find the 95% confidence interval for the true mean.

A) ($2.11, $5.34)
B) ($1.35, $2.85) C) ($4.81, $6.31) D) ($3.39, $6.01)

21) A local bank
needs information concerning the checking account balances of its customers. A
random sample of 15 accounts was checked. The mean balance was $686.75 with a
standard deviation of $256.20. Find a 98% confidence interval for the true
mean. Assume that the account balances are normally distributed.

A) ($487.31, $563.80)
B) ($238.23,
$326.41)

C) ($513.17, $860.33)
D) ($326.21, $437.90)

22) A survey of 100
fatal accidents showed that
43 were alcohol related. Find a point estimate for p, the
population proportion of accidents that were alcohol related.

A) 0.301 B) 0.43 C) 0.57 D) 0.754

23) A survey of 2290 golfers
showed that 306 of them are left-handed.
Find a point estimate for p, the population proportion of golfers that are
left-handed.

A) 0.866 B) 0.118 C) 0.154 D) 0.134

24) Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2280 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation

A) 4000 B) 0.
4300 C) 0.
5700 D) 2280

25) A survey of 400 non-fatal
accidents showed that 141 involved the
use of a cell phone. Construct a 99% confidence interval for the proportion of
fatal accidents that involved the use of a cell phone.

26) An article a
Florida newspaper reported on the topics that teenagers most want to discuss
with their parents. The findings, the results of a poll, showed that 46% would
like more discussion about the family's financial situation, 37% would like to
talk about school, and 30% would like to talk about religion. These and other
percentages were based on a national sampling of 549 teenagers. Estimate the proportion
of all teenagers who want more family discussions about school. Use a 99% confidence
level.

A) .37 ± .053 B) .63 ± .002 C) .37 ± .002 D) .63 ± .053

27) A university
dean is interested in determining the proportion of students who receive some
sort of financial aid. Rather than examine the records for all students, the
dean randomly selects 200 students and finds that 118 of them are receiving
financial aid. Use a
98% confidence interval to estimate the true proportion of
students on financial aid.

A) .59 ± .564 B) .59 ± .006 C) .59 ± .081 D) .59 ± .003

28) A pollster
wishes to estimate the proportion of United States voters who favor capital
punishment. How large a sample is needed in order to be 90% confident that the sample
proportion will not differ from the true proportion by more than 2%?

A) 1692 B) 3383 C) 21 D) 1024

29) A researcher
wishes to estimate the number of households with two cars. How large a sample
is needed in order to be
98% confident that the sample proportion will not differ from the
true proportion by more than 5%? A
previous study indicates that the proportion of households with two cars is 20%.

A) 246 B) 435 C) 348 D) 7

30) A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following confidence interval: (0.438, 0.642).

Using the
information above, what size sample would be necessary if we wanted to estimate
the true proportion to within
5% using 95% reliability?

A) 385 B) 382 C) 400 D) 369

**Answers**

1) C 2) C 3) C 4) B 5) A 6) A 7) D 8) C 9) D 10) A 11) A 12) B 13) C 14) 11 15) D 16) D 17) C 18) C 19) B 20) D