Problems to Look over Chapter 6
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of
$677. Find the margin of error if c = 0.95.
Answer: D
A) $77
B) $2891
C) $7
D) $217.3
2) A random sample of 120 students has a test score average with a standard deviation of 9.2. Find the
margin of error if c = 0.98.
Answer: A
A) 1.985
B) 0.82
C) 0.18
3) Find the critical value zc that corresponds to a 95% confidence level.
A) ±1.96
B) ±2.33
C) ±2.575
B) (2.51, 3.53)
C) (2.31, 3.88)
3)
Answer: A
D) ±1.645
B) ($1987, $2346)
C) ($2904, $3337)
B) (189.4, 194.6)
C) (188.5, 195.6)
D) (187.3, 196.1)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
7) In a random sample of 60 computers, the mean repair cost was $150 with a standard
deviation of $36.
a) Construct the 99% confidence interval for the population mean repair cost.
($138, $162)
b) If the level of confidence was lowered to 95%, what will be the effect on the confidence
interval?
A decrease in the level of significance will increase the width of the cofidence interval
1
5)
D) ($210, $110)
6) A group of 40 bowlers showed that their average score was 192 with a standard deviation of 8. Find
the 95% confidence interval of the mean score of all bowlers.
Answer: B
A) (186.5, 197.5)
4)
D) (2.43, 3.79)
5) A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of
$677. Construct the confidence interval for the population mean, µ if c = 0.95. Answer: C
A) ($4812, $5342)
2)
D) 0.84
4) A random sample of 150 students has a grade point average with a mean of 2.86 and with a
standard deviation of 0.78. Construct the confidence interval for the population mean, µ, if c = 0.98.
Answer: A
A) (2.71, 3.01)
1)
7)
6)
8) The number of wins in a season for 32 randomly selected professional football teams are
listed below. Construct a 90% confidence interval for the true mean number of wins in a
season.
9
9
9
8
10 9
7
2
11 10 6
4
11 9
8
8
12 10 7
5
12 6
4
3
12 9
7
10 7
7
5
9
8)
(7.2, 8.8)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
9) The standard IQ test has a mean of 101 and a standard deviation of 16. We want to be 98% certain
that we are within 4 IQ points of the true mean. Determine the required sample size.
Answer: C
A) 188
B) 10
C) 87
D) 1
10) In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less
than two hours in estimating the average time it takes to install tile flooring. Previous contracts
indicate that the standard deviation is 4.5 hours. How large a sample must be selected? Answer: C
A) 5
B) 4
C) 20
B) 512
C) 141
10)
D) 19
11) In order to set rates, an insurance company is trying to estimate the number of sick days that full
time workers at an auto repair shop take per year. A previous study indicated that the standard
deviation was 2.8 days. How large a sample must be selected if the company wants to be 95%
confident that the true mean differs from the sample mean by no more than 1 day?
Answer: D
A) 1024
9)
11)
D) 31
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
12) Given the same sample statistics, which level of confidence will produce the narrowest
confidence interval: 75%, 85%, 90%, or 95%? Explain your reasoning.
12)
The 75% level of confidence will produce the narrowest confidence interval. As the level of
confidence decreases, Zc decreases, causign narrower intervals
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
13) Find the critical value, tc for c = 0.99 and n = 10. Use table in Textbook
A) 2.262
B) 3.25
C) 3.169
14) Find the value of E, the margin of error, for c = 0.90, n = 16 and s = 2.5.
A) 0.84
B) 0.21
C) 1.1
2
Answer: B
13)
D) 1.833
Answer: C
D) 0.27
14)
15) In a random sample of 28 families, the average weekly food expense was $95.60 with a standard
deviation of $22.50. Determine whether a normal distribution or a t-distribution should be used or
whether neither of these can be used to construct a confidence interval. Assume the distribution of
weekly food expenses is normally shaped.
Answer: C
because n<30
15)
A) Cannot use normal distribution or t-distribution.
B) Use normal distribution.
C) Use the t-distribution.
16) A random sample of 40 college students has a mean earnings of $3120 with a standard deviation of
$677 over the summer months. Determine whether a normal distribution or a t-distribution should
be used or whether neither of these can be used to construct a confidence interval. Answer: C
because n>=30
A) Cannot use normal distribution or t-distribution.
B) Use the t-distribution.
C) Use normal distribution.
3
16)