Download Statistics Chapters 7, 8, 9, 10 and 11

Supplemental Instruction Handouts
Statistics
Chapters 7, 8, 9, 10 and 11
1.
The weekly incomes of a large group of middle managers are normally distributed with a mean of $800 and
a standard deviation of $45.
A)
B)
C)
D)
E)
F)
G)
2.
Based on previous experience 2% of the valve seats for a certain type of butterfly valve are known to be
defective as they come off the production line. We are going to select 1000 valves for inspection.
A)
B)
C)
D)
E)
F)
G)
3.
What is the probability of finding a middle manager with a weekly income of between $840 and
$900?
What is the percent of middle managers that earn more than $905?
What is the percent of middle managers that earn less than $905?
What is the probability of finding a middle manager with a weekly income of between $750 and
$850?
What is the probability of finding a middle manager with a weekly income of between $700 and
$790?
Above what income would the top 10% of the managers earn?
Below what income would the lowest 10% of the managers earn?
What is the mean?
What is the standard deviation?
What is the probability that there will be more than 24 defective valves?
What is the probability that there will be less than 18 defective valves?
What is the probability that there will be 16 or less defective valves?
What is the probability that there will be 26 or more defective valves?
What is the probability that there will be exactly 20 defective valves?
Your company has five salespeople. Here is the list of those salespeople and the number of cars they sold
last week:
Name
Bruce
Damien
Joelle
Joshua
Melissa
A)
B)
C)
D)
E)
Sales
18
22
15
14
17
How many samples of size 2 are possible?
List all samples of size 2 and compute the mean for each sample.
Compute the mean of the sample distribution.
Compute the mean of the population distribution.
Is there a difference between the mean of the sample distribution and the population
distribution?
Academic Success Centre
www.rrc.mb.ca/asc
These questions were compiled by Michael Reimer for the Academic Success Centre.
4.
The mean rent for a one – bedroom apartment in Winnipeg is $800 per month with a standard deviation of
$125. If we were to select 40 apartments:
A)
B)
C)
D)
What is the standard error of the mean?
What would be the probability the mean would be less than $750?
What would be the probability the mean would be greater than $825?
What would be the probability that the mean is between $765 and $835?
5.
Al Fisher is the owner of Al’s Marathon gas station. Al would like to estimate the mean number of gallons of
gasoline sold to his customers. From his records he selects a sample of 80 sales and finds that the mean
number of gallons sold is 8.6. The population standard deviation is 2.3 gallons. Develop a 99% confidence
interval for the population mean.
6.
A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes
during a week. A sample of 25 steady smokers revealed that the mean was $20 with a standard deviation of
$5.
A)
B)
7.
Develop a 99% confidence interval for the amount of money spent by steady smokers.
If a local grocery store has a customer base of 400 steady smokers, develop a 99% confidence
interval for the amount of money spent by steady smokers.
A silkscreen printer purchases plastic cups on which to print logos for sporting events and other special
occasions. The printer received a large shipment this morning and would like to estimate the percent
defective. A sample of 200 revealed 30 of the cups to be defective.
A)
B)
Develop a 95% confidence interval for the estimate of the percent defective.
If the silkscreen printer purchased 2000 plastic cups in total, estimate the percent defective using
a 95% confidence interval.
8.
Suppose the breaking strength of cables (in pounds) is known to have a normal distribution with a standard
deviation of 6 pounds. Find how large a sample must be taken so as to be 90 percent confident that the
sample mean breaking strength will not differ from the true mean breaking strength by more than 0.75
pounds.
9.
A coffee company wants to estimate the true proportion in the Canadian population that drinks its brand.
How many individuals should be surveyed to be 99 percent confident of having the true proportion of
people drinking the brand estimated to within 0.017?
10.
A breeder of rabbit’s claims that he can breed rabbits yielding a mean weight of greater than 58 ounces.
Suppose the standard deviation is known to be 3 ounces. A random sample of 32 rabbits had a mean
weight of 59.2 ounces. Can we conclude that the breeder is breeding rabbits yielding a mean weight that is
greater than 58 ounces? (Use the 5% level of significance.)
A)
B)
C)
D)
E)
F)
Is this a one – tailed or two – tailed test?
State the null hypothesis and the alternate hypotheses.
Compute the critical value(s).
Compute the value of the test statistic.
What is your decision?
What is the p-value?
Academic Success Centre
www.rrc.mb.ca/asc
These questions were compiled by Michael Reimer for the Academic Success Centre.
11.
A ski coach claims that she can train beginning skiers for 3 weeks so that at the end of the program they will
finish a certain downhill course in less than 13 minutes. It was found that, when a random sample of ten
skiers was given the training, their mean time was 12.3 minutes with a standard deviation of 1.2 minutes.
On the basis of this evidence, is the true mean time significantly less than 13 minutes? (Use the 2.5 percent
level of significance.)
A)
B)
C)
D)
E)
F)
12.
A recent article in the Winnipeg Free Press reported that a job awaits only one in three new college
graduates. The major reasons given were an overabundance of college graduates and a weak economy. A
survey of 200 recent graduates from RRC revealed that 80 students had jobs. At the 2 percent level of
significance, can we conclude that a larger proportion of students at RRC have jobs?
A)
B)
C)
D)
E)
F)
13.
Is this a one – tailed or two – tailed test?
State the null hypothesis and alternate hypotheses.
Compute the critical value(s).
Compute the value of the test statistic.
What is your decision?
What is the p – value?
The Metro Real Estate Association is preparing a pamphlet that they feel might be of interest to prospective
homebuyers in the Westwood and Crestview areas of the city. One item of interest is the length of time the
seller occupied the home. The standard deviation for Westwood is 2.3 years and the standard deviation for
Crestview is 2.9 years. A sample of 40 homes sold recently in Westwood revealed that the mean length of
ownership was 7.6 years. A sample of 55 homes in Crestview revealed that the mean length of ownership
was 8.1 years. At the 2 percent level of significance, can we conclude that there is a difference in length of
ownership between the two areas of the city?
A)
B)
C)
D)
E)
F)
14.
Is this a one – tailed or a two – tailed test?
State the null hypothesis and the alternative hypotheses.
Compute the critical value(s).
Compute the value of the test statistic.
What is your decision?
What is the p - value?
Is this a one – tailed or two – tailed test?
State the null hypothesis and the alternative hypotheses.
Compute the critical value(s).
Compute the value of the test statistic.
What is your decision?
What is the p – value?
A survey was conducted to compare the proportions of males and females who favor government
assistance for child care. It was found that among 64 males interviewed, 40 favored assistance, and among
100 females, 70 favored assistance. At the 5 percent level of significance, are the true proportions among
males and females in the population who favor government assistance for child care significantly different?
A)
B)
C)
D)
E)
F)
Is this a one – tailed or two – tailed test?
State the null and alternative hypotheses.
Compute the critical value(s).
Compute the value of the test statistic.
What is your decision?
What is the p – value?
Academic Success Centre
www.rrc.mb.ca/asc
These questions were compiled by Michael Reimer for the Academic Success Centre.
15.
You have been asked to check to see if the bottles being filled by Abe are greater than the bottles that are
being filled by Bev. You select a sample of 28 bottles filled by Abe and find that the average weight of the
bottles is 8.35 ounces with a standard deviation of 1.27 ounces. You then select a sample of 26 bottles filled
by Bev and find that the average weight of the bottles is 7.85 ounces with a standard deviation of 1.41
ounces. At the 0.05 level of significance, is the mean weight of the bottles filled by Abe’s machine greater
than the mean weight of the bottles filled by Bev’s machine?
A)
B)
C)
D)
E)
F)
16.
Is this a one – tailed or two – tailed test?
State the null and alternative hypothesis.
Compute the critical value(s).
Compute the value of the test statistic.
What is your decision?
What is the p – value?
A survey is to be conducted at RRC to measure the effect of the change in environment on foreign students.
One of the facets of the study is a comparison of student weights upon arrival on campus with weights one
year later. It is hypothesized that the richer Canadian food will cause an increase in weight. The 1 percent
level of significance is to be used. A random sample of 11 foreign students is chosen for the study. Has the
richer Canadian food caused an increase in the foreign students’ weights?
Name
Nassar
O’Toole
Obie
Silverman
Kim
Gross
Farouk
Thatcher
Sambul
Onassis
Pierre
A)
B)
C)
D)
E)
F)
Weight on
Arrival
124
157
98
190
103
135
149
176
200
180
256
Weight one
Year Later
142
157
96
212
116
134
150
184
209
180
269
Is this a one – tailed or two – tailed test?
State the null and alternative hypothesis.
Compute the critical value(s).
Compute the value of the test statistic.
What is your decision?
What is the p – value?
Academic Success Centre
www.rrc.mb.ca/asc
These questions were compiled by Michael Reimer for the Academic Success Centre.