The following are practice problems that I need help answering in
preparation for a Statistics exam coming up. All of the information
enclosured here is ficticous. If you could please help me by answering
the enitre set. Please ask me any questions that you may have.
Thank you!
1.
15. WNAE, an all-news AM station, finds that the distribution of the
lengths of time listeners are tuned to the station follows the normal
distribution. The mean of the distribution is 15.0 minutes and the
standard deviation is 3.5 minutes. What is the probability that a
particular
listener will tune in:
a. More than 20 minutes?
b. For 20 minutes or less?
c. Between 10 and 12 minutes?
2.
16. The mean starting salary for college graduates in the spring of
2000 was $31,280. Assume that the distribution of starting salaries
follows the normal distribution with a standard deviation of $3,300.
What percent of the graduates have starting salaries:
a. Between $30,000 and $35,000?
b. More than $40,000?
c. Between $35,000 and $40,000?
3.
49. The Georgetown, South Carolina, Traffic Division reported 40
percent of the high-speed chases involving automobiles result in a
minor or major accident. During a month in which 50 high-speed chases
occur, what is the probability that 25 or more will result in a minor
or major accident?
4.
55. The weights of canned hams processed at the Henline Ham Company
follow the normal distribution, with a mean of 9.20 pounds and a
standard deviation of 0.25 pounds. The label weight is given as 9.00
pounds.
a. What proportion of the hams actually weigh less than the amount
claimed on the label?
b. The owner, Glen Henline, is considering two proposals to reduce the
proportion of hams below label weight. He can increase the mean weight
to 9.25 and leave the standard deviation the same, or he can leave the
mean weight at 9.20 and reduce the standard deviation from 0.25 pounds
to 0.15. Which change would you recommend?
5.
15. The mean rent for a one-bedroom apartment in Southern California
is $1,200 per month.The distribution of the monthly costs does not
follow the normal distribution. In fact, it is positively skewed. What
is the probability of selecting a sample of 50 one-bedroom apartments
and finding the mean to be at least $950 per month. The standard
deviation of the
sample is $250.
6.
16. According to an IRS study, it takes an average of 330 minutes for
taxpayers to prepare, copy, and mail a 1040 tax form. A consumer
watchdog agency selects a random sample of 40 taxpayers and finds the
standard deviation of the time to prepare, copy, and mail form 1040 is
80 minutes.
a. What assumption or assumptions do you need to make about the shape of the
population?
b. What is the standard error of the mean in this example?
c. What is the likelihood the sample mean is greater than 320 minutes?
d. What is the likelihood the sample mean is between 320 and 350 minutes?
e. What is the likelihood the sample mean is greater than 350 minutes?
7.
23. A study of motel facilities in a metropolitan area showed there
were 25 facilities. The city?s convention and visitors bureau is
studying the number of rooms at each location. The results are as
follows:
90 72 75 60 75 72 84 72 88 74 105 115 68 74 80 64 104 82 48 58 60 80 48 58 100
a. Using a table of random numbers (Appendix E), select a random
sample of five motels from this population.
b. Obtain a systematic sample by selecting a random starting point
among the first five motels and then select every fifth motel.
c. Suppose the last five motels are ?cut-rate? motels. Describe how
you would select a random sample of three regular motels and two
cut-rate motels.
8.
34. A recent study by the Greater Los Angeles Taxi Drivers Association
showed that the mean fare charged for service from Hermosa Beach to
the Los Angeles International Airport is $18.00 and the standard
deviation is $3.50. We select a sample of 15 fares.
a. What is the likelihood that the sample mean is between $17.00 and $20.00?
b. What must you assume to make the above calculation?
9.
7. Bob Nale is the owner of Nale?s Texaco GasTown. Bob would like to
estimate the mean number of gallons of gasoline sold to his customers.
From his records, he selects a random sample of 60 sales and finds the
mean number of gallons sold is 8.60 and the standard deviation is 2.30
gallons.
a. What is the point estimate of the population mean?
b. Develop a 99 percent confidence interval for the population mean.
c. Interpret the meaning of part b.
10.
8. Dr. Patton is a Professor of English. Recently he counted the
number of misspelled words in a group of student essays. For his class
of 40 students, the mean number of misspelled words was 6.05 and the
standard deviation 2.44 per essay. Construct a 95 percent confidence
interval for the mean number of misspelled words in the population of
students.
11.
46. Furniture Land South surveyed 600 consumers and found that 414
were enthusiastic about a new home décor they plan to show in their
store in High Point, North Carolina. Construct the 99 percent
confidence interval for the population proportion.
12.
53. You are to conduct a sample survey to determine the mean family
income in a rural area of central Florida. The question is, how many
families should be sampled? In a pilot sample of 10 families, the
standard deviation of the sample was $500. The sponsor of the survey
wants you to use the 95 percent confidence level. The estimate is to
be within $100. How many families should be interviewed?
13.
17. Experience raising New Jersey Red chickens revealed the mean
weight of the chickens at five months is 4.35 pounds. The weights
follow the normal distribution. In an effort to increase their weight,
a special additive is added to the chicken feed. The subsequent
weights of a sample of five-month-old chickens were (in pounds):
4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39
At the .01 level, has the special additive increased the mean weight
of the chickens? Estimate the p-value.
14.
21. The following hypotheses are given.
H0: pie is less than/equal to .70
H1: pie is greater than .70
A sample of 100 observations revealed that p =.75. At the .05
significance level, can the null hypothesis be rejected?
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis?
15.
25. Chicken Delight claims that 90 percent of its orders are delivered
within 10 minutes of the time the order is placed. A sample of 100
orders revealed that 82 were delivered within the promised time. At
the .10 significance level, can we conclude that less than 90 percent
of the orders are delivered in less than 10 minutes?
16.
26. Research at the University of Toledo indicates that 50 percent of
the students change their major area of study after their first year
in a program. A random sample of 100 students in the College of
Business revealed that 48 had changed their major area of study after
their first year of the program. Has there been a significant decrease
in the proportion of students who change their major after the first
year in this program? Test at the .05 level of significance.
17.
13. The null and alternate hypotheses are:
H0: pie sub1 ? pie sub2
H1: pie sub1 > pie sub2
A sample of 100 observations from the first population indicated that
X1 is 70. A sample of 150 observations from the second population
revealed X2 to be 90. Use the .05 significance level to test the
hypothesis.
a. State the decision rule.
b. Compute the pooled proportion.
c. Compute the value of the test statistic.
d. What is your decision regarding the null hypothesis?
18.
14. The null and alternate hypotheses are:
H0: pie sub1 = pie sub2
H1: pie sub1 (is not equal to) pie sub2
A sample of 200 observations from the first population indicated that
X1 is 170. A sample of 150 observations from the second population
revealed X2 to be 110. Use the .05 significance level to test the
hypothesis.
a. State the decision rule.
b. Compute the pooled proportion.
c. Compute the value of the test statistic.
d. What is your decision regarding the null hypothesis?
19.
25. An official of the Iowa Department of Highways wants to compare
the useful life, in months, of two brands of paint used for striping
roads. The mean number of months Cooper Paint lasted was 36.2, with a
standard deviation of 1.14 months. The official reviewed 35 road
stripes. For King Paint, the mean number of months was 37.0, with a
standard deviation of 1.3 months. The official reviewed 40 road
stripes. At the .01 significance level, is there a difference in the
useful life of the two paints? Compute the p-value.
20.
26. Clark Heter is an industrial engineer at Lyons Products. He would
like to determine whether there are more units produced on the
afternoon shift than on the day shift. A sample of 54 day-shift
workers showed that the mean number of units produced was 345, with a
standard deviation of 21. A sample of 60 afternoon-shift workers
showed that the mean number of units produced was 351, with a standard
deviation of 28 units. At the .05 significance level, is the number of
units produced on the afternoon shift larger?
21.
44. Two boats, the Sea Hawk and the Sea Queen, are competing for a
spot in the upcoming America?s Cup race. To decide which will
represent the United States, they race over a part of the course
several times. Below are the sample times in minutes. At the .05
significance level, can we conclude that there is a difference in
their mean times?
Boat Times (minutes)
Sea Hawk 12.9 12.5 11.0 13.3 11.2 11.4 11.6 12.3 14.2 11.3
Sea Queen 14.1 14.1 14.2 17.4 15.8 16.7 16.1 13.3 13.4 13.6 10.8 19.0 |
