Assignment 8 Fall 2023 (1)
docx
keyboard_arrow_up
School
James Madison University *
*We aren’t endorsed by this school
Course
191
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
Pages
11
Uploaded by AdmiralField5381
COB 191 Assignment 8
Due:12/08/2023
Refer to this chart for questions 1 - 3.
1. What percent of employees sold less than $20 million?
a.
20%
b.
30%
c.
60%
d.
70%
e.
80%
2. How many employees had at least $10 million in sales?
a.
40 employees
b.
60 employees
c.
120 employees
d.
160 employees
e.
180 employees
3. 90% of the salespeople had at least in annual sales.
a.
$5 million
b.
$10 million
c.
$15 million
d.
$20 million
e.
$25 million
The histogram below represents the annual sales of a sample of 200 sales employees for a large firm.
Annual Sales per Salesperson
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0 to 5-5 to 10-10 to 15-15 to 20-20 to 25-25 to 30-
Sales (millions of dollars)
relative frequency
Refer to the following data for questions 4 - 6.
4. The median number of grams of carbohydrate is:
a.
16
b.
17.5
c.
18.5
d.
19
e.
24
5.
The range of the sample is
a.
5
b.
10
c.
11
d.
17
e.
30
6. Suppose A and B are independent events where P(A) = 0.4, P(B) = 0.5 and P(A and B)
= 0.2 then P(A | B) =
a.
0.02
b.
0.10
c.
0.20
d.
0.40
e.
0.80
The 11 numbers below represent the number of grams of carbohydrates in one serving of 11 different breakfast cereals.
13
15
24
30
21
16
19
24
16
24
18
The mean of these values is 20.
Questions 7 - 9 refer to the information below.
7.
What is the probability that a randomly selected individual is single and under 30?
a.
14/140
b.
21/140
c.
28/140
d.
77/140
e.
105/140
8.
If a randomly selected individual is married, what is the probability that this
individual is 30 or older?
a.
14/35
b.
77/105
c.
28/105
d.
21/35
e.
21/49
9. If two events are mutually exclusive, the probability of their intersection, that is,
P (A and B) , is equal to
a.
0
b.
0.50
c.
P(A)
P(B)
d.
P(A) + P(B)
e.
Cannot be determined from the information given.
A survey is taken among customers of a popular nightclub to determine patrons’ age and marital status. Of the 140 respondents selected, 91 were under 30 and 105 were single. 21
of the married customers were 30 or older.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
10. In a binomial distribution
a.
the random variable X is continuous.
b.
the
probability
of
success p
is
stable
from
trial
to
trial.
c.
the number of trials n must be at least 30.
d.
the results of one trial are dependent on the results of the other trials.
e.
All of these statements (a-d) are true.
11. On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store. What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter
during a given minute of time?
a.
binomial distribution
b.
Poisson
distribution
c.
normal distribution
d.
F distribution
e.
chi-squared distribution
12. The local police department must write on average 5 tickets a day to keep department
revenues at budgeted levels. Suppose the number of tickets written per day follows a
Poisson distribution with a mean of 6 tickets per day. Interpret the value of the mean.
a.
The number of tickets that is written most often is 6 tickets per day.
b.
About half of the days have less than 6 tickets written and about half of the days
have more than 6 tickets written.
c.
If
we
recorded
the
number
of
tickets
written
each
day
for
a
long
period
of time, the arithmetic average of these values would be very close to 6.
d.
6 tickets are written every day.
e.
The number of tickets written on any day is within 6 tickets of the number of
tickets written on any other day.
13. The standard error of the mean
a.
is never larger than the standard deviation of the population.
b.
decreases as the sample size increases.
c.
measures the variability of the mean from sample to sample.
d.
is used to construct the confidence interval for
.
e.
All
of
the
above.
14. The Central Limit Theorem is important in statistics because it says that
a.
for a large n, the population is always approximately normal.
b.
for any population, the sampling distribution of the mean is approximately normal.
c.
for
a
large
n,
the
sampling
distribution
of
the
mean
is
approximately
normal.
d.
for any binomial population, the sampling distribution of the mean is approximately normal.
e.
if the sampling distribution of the mean is normal, then so is the population.
15. At a computer manufacturing company, the actual size of computer chips is normally
distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A
random sample of 12 computer chips is taken. What is the standard error for the sample mean?
a.
0.029
b.
0.050
c.
0.091
d.
0.100
e.
0.120
16. In a certain problem, the standard error of the mean for a sample of 100 is 30. In
order to cut the standard error of the mean to 15, we would
a.
increase the sample size to 115.
b.
increase the sample size to 200.
c.
increase
the
sample
size
to
400.
d.
decrease the sample size to 50.
e.
decrease the sample to 25.
17. The number of violent crimes committed in a day possesses a distribution with a population mean of 1.5 crimes per day and a population standard deviation of 4 crimes per day. Suppose a large number of random samples of 100 days each were drawn from this population and for each sample the mean number of crimes per day was calculated. If a histogram of these sample means were created we would expect it
to be:
a.
approximately normal with mean = 1.5 standard deviation = 4
b.
shape unknown with mean = 1.5 and standard deviation = 4
c.
approximately
normal
with
mean
=
1.5
and
standard
deviation
= 0.4
d.
shape unknown with mean = 1.5 and standard deviation = 0.4
e.
approximately normal, with a mean of 0.15 and a standard deviation of 4.
18. X is normally distributed with a mean of 32 and a standard deviation of 8. What
Excel calculation would give the probability that X is greater than 43?
a. =NORMSINV(0.25)
b. =NORMSDIST(1.375)
c. =NORMSINV(5.375)
d. =1 – NORMSDIST(1.375)
e. =1 -
NORMSDIST(5.375)
19. Consider this question: “
What interval (centered on 100) will contain 80% of all observations in a normally distributed population with a mean of 100 and a standard
deviation of 10?
” Which of the following calculations would provide the upper cutoff for this range?
a. = NORMSINV (0.8) * 10
b. = NORMSINV(0.9) * SQRT(10)
c. = TINV( 0.8, 99) * 100
d. =
100
+
NORMSINV(0.8)
*
SQRT(10)
e. = 100 + NORMSINV(0.9) * 10
20. Consider this question: “
According to government data, 25% of employed women have never been married. If 5 employed women are selected at random, what is the
probability that exactly 2 have never been married?
” Which of the following calculations would provide the answer to this question? (You may assume that the population of employed women is essentially infinite.)
a. = NORMSINV(0.25) * SQRT((0.4*0.6)/5)
b. = NORMSINV(0.4) * SQRT((0.25*0.75)/5)
c. =
BINOMDIST(2,
5,
0.25,
TRUE)
d.
= BINOMDIST(2, 5, 0.25, FALSE)
e. = BINOMDIST(0.4, 5, 0.75, TRUE)
21. Consider this question: “
Suppose that, on average, three customers arrive per minute
at a bank during the noon hour. What is the probability that two customers will arrive in a given minute
?” An Excel computation giving the answer is
a. = BINOMDIST(2, 3, 2, FALSE)
b.
= BINOMDIST(2, 3, 2, TRUE)
c. =
POISSON(2,
3,
FALSE)
d. = NORMSDIST(2/3)
e. = TDIST(2, 3, 2)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
22. A is the corresponding statistic that is used to estimate
the parameter of interest.
a.
point estimate
b.
sampling fraction
c.
sample coefficient
d.
population proxy
e.
null parameter
Use this information for problems 23 and 24.
23. What is the parameter of interest for this problem?
a.
population percentage
b.
sample standard deviation
c.
population
mean
d.
sample mean
e.
population standard deviation
24. If the manager constructs a confidence interval for this problem, what would be the
purpose of doing so?
a.
to
estimate
the
parameter
of
interest
b.
to estimate the sample proportion
c.
to estimate the sample mean
d.
both a and b
e.
both b and c
The quality control manager at a light bulb factory needs to estimate the average life of a shipment of light bulbs. The shipment standard deviation for the life of these light bulbs is known to be 100 hours. A random sample of 50 light bulbs taken from the shipment yields a sample average life of 350 hours. The manager wishes to set up an 85% confidence interval estimate of the true average life of light bulbs in this shipment.
25. The owner of a small deli wants to estimate the population mean expenditure for customers at the deli. The population standard deviation is $2.25. The expenditure
per customer is normally distributed. A sample of size 16 is selected and yields a mean expenditure per customer of $7.20. The 95% confidence interval for the population mean is
a.
$3.51 to $10.89
b.
$4.95 to $9.45
c.
$6.10 to $8.30
d.
$6.27 to $8.13
e.
$6.48 to $7.92
26. Which of the following is most closely synonymous with the term “standard error”?
a.
standard deviation of the population
b.
standard deviation of the sample
c.
standard
deviation
of
the sampling
distribution
d.
sampling error
e.
estimator bias
27. Which of the following statements could correctly be used as the null hypothesis for
an hypothesis test?
i.
The mean of the population is equal to 55.
ii.
The mean of the sample is equal to 55.
iii.
The mean of the population is greater than 55.
a.
I
only
b. II only
c. III only
d. I and III only
e. II and III only
28. If an economist wishes to determine if there is evidence that average family income in a community exceeds $25,000
a.
either a one-tailed or two-tailed test could be used.
b.
a
one-tailed
test
should
be
used,
with
rejection
occurring
in
the
upper
tail.
c.
a one-tailed test should be used, with rejection occurring in the lower tail.
d.
a two-tailed test should be used.
e.
the number of tails used depends on whether variances can be assumed equal.
Use this information for questions 29-31:
29. What is the null and hypothesis?
a.
Ho: µ = 8.81
b.
Ho:
µ
=
8.89
c.
Ho: µ
8.81
d.
Ho: µ
8.89
e.
Ho: µ >
8.89
30. Which calculation would give the (upper) critical value for the test statistic?
a. = NORMSINV(0.11)
b. = NORMSINV(0.89)
c. = NORMSINV(0.945)
d. = TINV(0.11, 23)
e. = TINV(0.89, 23)
31. Which calculation would give the test statistic value (t or z) for this sample?
a. = 8.89 - 8.81/(24*0.2)
b. = (8.89 – 8.81)/SQRT(0.2)
c. = (8.89
– 8.81)/SQRT(24)
d. = (8.89 – 8.81)/(0.2/SQRT(24))
e. = (8.89 – 8.81)/0.2
A chemical process is set to produce an average of 8.81 tons per hour with a population standard deviation of 0.20 tons. The population is normally distributed. The most recent sample of n = 24 show an average production of 8.89 tons. Hypothesis testing at the 0.11 level of significance will be performed by the manager to see if the process average has changed.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Use this information for questions 32 through 35:
32. What are the null and alternate hypothesis?
a.
Ho: p <
0.44 versus H
1
: p > 0.44
b.
Ho:
p
<
0.40
versus
H
1
:
p
>
0.40
c.
Ho: p < 0.40 versus H
1
: p >
0.40
d.
Ho: p < 0.44 versus H
1
: p >
0.44
e.
Ho: p = 0.40 versus H
1
:
p
0.40
33. If you were to do this hypothesis test by using the p-value approach, the first step toward computing that p would be to compute the standard error of the proportion. What calculation would provide the value of the standard error of the proportion?
a. =
SQRT(0.4*0.6/500)
b. = SQRT(0.44*0.56/500)
c. = (0.44-0.400)/SQRT(500)
d. = (220 – 200)/SQRT(500)
e. = SQRT(200/220)
34. If you were to do this hypothesis test by using the p-value approach, your second step would be to compute the z-score of your test statistic. You would compute the z
rather than the t because
a.
the
population
standard
deviation
is
known
b.
the population standard deviation is unknown
c.
the problem involves a single population
d.
the problem involves two populations
e.
the problem involves proportions
The marketing branch of the Mexican Tourist Bureau would like to increase the percentage of tourists who purchase silver jewelry while in Mexico from its present estimated population percentage of 40%. Toward this end, promotional literature describing the beauty of the jewelry is distributed to all passengers on airplanes arriving at a seaside resort during a one-week period. A sample of 500 passengers returning at the end of the one-week period is randomly selected, and 220 of these passengers indicate that they have purchased jewelry. At the .05 level of significance, the Tourist Bureau wishes to conduct an hypothesis to see if there is evidence that the proportion of tourists buying silver jewelry has increased above the previous value of 40%.
35. If you were to do this hypothesis test by using the p-value approach, your third step would be to compute the p statistic from your sample based on the z score that you found in problem 51. Pretend that this z-statistic turned out to be 3.5. Then correct p score for this sample in this upper tailed test is given by the Excel calculation
a. = NORMSDIST(3.5)
b
.
=
1
-
NORMSDIST(3.5)
c. = 2 * NORMSDIST(3.5)
d. = 0.5 * NORMSDIST(3.5)
e. = 0.4 * NORMSDIST(3.5)