MATH221 Statistics for Decision Making
Week 6 Homework
Question 1A
consumer analyst reports that the mean life of a certain type of alkaline
battery is more than 63 months. Write the null and alternative hypotheses and
note which is the claim.
Homework
Help:
6DA. Theory
and basics of writing hypotheses (Links to an external site.) (DOCX)
Ho: ? ? 63, Ha: ? < 63 (claim)
Ho: ? = 63 (claim), Ha: ? ? 63
Ho: ? ? 63, Ha: ? > 63 (claim)
Ho: ? > 63 (claim), Ha: ? ? 63
Question 2A
business claims that the mean time that customers wait for service is at most
5.9 minutes. Write the null and alternative hypotheses and note which is the
claim.
Homework
Help:
6DA. Theory
and basics of writing hypotheses (Links to an external site.) (DOCX)
Ho: ? > 5.9 (claim), Ha: ? > 5.9
Ho: ? ? 5.9, Ha: ? ? 5.9 (claim)
Ho: ? ? 5.9 (claim), Ha: ? > 5.9
Ho: ? > 5.9, Ha: ? ? 5.9 (claim)
Question 3An
amusement park claims that the average daily attendance is at least 20,000.
Write the null and alternative hypotheses and note which is the claim.
Homework
Help:
6DA. Theory
and basics of writing hypotheses (Links to an external site.) (DOCX)
Ho: ? > 20000 (claim), Ha: ? = 20000
Ho: ? ? 20000, Ha: ? > 20000 (claim)
Ho: ? ? 20000 (claim), Ha: ? < 20000
Ho: ? = 20000, Ha: ? ? 20000 (claim)
Question 4A transportation organization claims
that the mean travel time between two destinations is about 23 minutes. Write
the null and alternative hypotheses and note which is the claim.
Homework
Help:
6DA. Theory
and basics of writing hypotheses (Links to an external site.) (DOCX)
Ho: ? > 23, Ha: ? ? 23 (claim)
Ho: ? ? 23, Ha: ? = 23 (claim)
Ho: ? = 23 (claim), Ha: ? ? 23
Ho: ? = 23 (claim), Ha: ? ? 23
Question 5If
the null hypothesis is not rejected when it is false, this is called
__________.
Homework
Help:
6DB. Type I
and type II errors (Links to an external site.) (DOCX)
the Empirical Rule
an alternative hypothesis
a type I error
a type II error
Question 6A
scientist claims that the mean gestation period for a fox is more than 48.9
weeks. If a hypothesis test is performed that rejects the null hypothesis, how
would this decision be interpreted?
Homework
Help:
6VA.
Overview of hypothesis testing: hypotheses, conclusions, implications for claim
(Links to an external site.)(4:32)
6DC.
Connecting reject/fail to reject decision and implication for claim (Links to
an external site.) (DOCX)
There is enough evidence to support the
scientist’s claim that the gestation period is more than 48.9 weeks
There is not enough evidence to support the
scientist’s claim that the gestation period is 48.9 weeks
The evidence indicates that the gestation
period is less than 48.9 weeks
There is enough evidence to support the
scientist’s claim that the gestation period is 48.9 weeks
Question 7A
marketing organization claims that less than 15% of its employees are paid
minimum wage. If a hypothesis test is performed that fails to reject the null
hypothesis, how would this decision be interpreted?
Homework
Help:
6VA.
Overview of hypothesis testing: hypotheses, conclusions, implications for claim
(Links to an external site.)(4:32)
6DC.
Connecting reject/fail to reject decision and implication for claim (Links to
an external site.) (DOCX)
There is not sufficient evidence to support
the claim that less than 15% of the employees are paid minimum wage
There is sufficient evidence to support the
claim that less than 15% of the employees are paid minimum wage
There is sufficient evidence to support the
claim that 15% of the employees are paid minimum wage
There is not sufficient evidence to support
the claim that more than 15% of the employees are paid minimum wage
Question 8A
sprinkler manufacturer claims that the average activating temperatures is at
least 131 degrees. To test this claim, you randomly select a sample of 32
systems and find the mean activation temperature to be 133 degrees. Assume the
population standard deviation is 3.3 degrees. Find the standardized test
statistic and the corresponding p-value.
Homework
Help:
6VB.
Hypothesis testing with spreadsheet to find test statistic and p-value (Links
to an external site.) (2:58)
z-test statistic = -3.43, p-value = 0.0003
z-test statistic = 3.43, p-value = 0.0006
z-test statistic = -3.43, p-value = 0.0006
z-test statistic = 3.43, p-value = 0.0003
Question 9A
consumer group claims that the mean acceleration time from 0 to 60 miles per
hour for a sedan is 7.9 seconds. A random sample of 33 sedans has a mean
acceleration time from 0 to 60 miles per hour of 7.6 seconds. Assume the
population standard deviation is 2.3 seconds. Find the standardized test
statistic and the corresponding p-value.
Homework
Help:
6VB.
Hypothesis testing with spreadsheet to find test statistic and p-value (Links
to an external site.) (2:58)
z-test statistic = -0.749, p-value = 0.227
z-test statistic = -0.749, p-value = 0.454
z-test statistic = -0.749, p-value = 0.227
z-test statistic = 0.749, p-value = 0.454
Question 10A
consumer research organization states that the mean caffeine content per
12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams.
You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that
has a mean caffeine content of 35.2 milligrams. Assume the population standard
deviation is 12.5 milligrams. At ?=0.05, do you support or reject the
organization’s claim using the test statistic?
Homework
Help:
6VC.
Determining when to reject or fail to reject, both methods (Links to an
external site.) (4:00)
6VE. Second
sample hypothesis testing from word problem to implications for claim, with
test statistic (Links to an external site.) (3:26)
6DD.
Determining when to reject or fail to reject, both methods (Links to an
external site.) (DOCX)
Claim is null, fail to reject the null and
support claim as test statistic (-1.44) is not in the rejection region defined
by the critical value (-1.96)
Claim is alternative, fail to reject the null
and support claim as test statistic (-1.44) is not in the rejection region
defined by the critical value (-1.64)
Claim is alternative, reject the null and
reject claim as test statistic (-1.44) is in the rejection region defined by
the critical value (-1.64)
Claim is null, reject the null and reject
claim as test statistic (-1.44) is in the rejection region defined by the
critical value (-1.96)
Question 11A
computer manufacturer estimates that its cheapest screens will last less than
2.8 years. A random sample of 61 of these screens has a mean life of 2.6 years.
The population is normally distributed with a population standard deviation of
0.88 years. At ?=0.02, what type of test is this and can you support the
organization’s claim using the test statistic?
Homework
Help:
6VC.
Determining when to reject or fail to reject, both methods (Links to an
external site.) (4:00)
6VE. Second
sample hypothesis testing from word problem to implications for claim, with
test statistic (Links to an external site.) (3:26)
6DD.
Determining when to reject or fail to reject, both methods (Links to an
external site.) (DOCX)
Claim is null, fail to reject the null and
cannot support claim as test statistic (-1.78) is not in the rejection region
defined by the critical value (-2.05)
Claim is alternative, reject the null and
support claim as test statistic (-1.78) is not in the rejection region defined
by the critical value (-2.05)
Claim is alternative, fail to reject the null
and cannot support claim as test statistic (-1.78) is not in the rejection
region defined by the critical value (-2.05)
Claim is null, reject the null and cannot
support claim as test statistic (-1.78) is not in the rejection region defined
by the critical value (-2.05)
Question 12A
pharmaceutical company claims that the average cold lasts an average of 8.4
days. They are using this as a basis to test new medicines designed to shorten
the length of colds. A random sample of 106 people with colds, finds that on
average their colds last 8.5 days. The population is normally distributed with
a population standard deviation of 0.9 days. At ?=0.02, what type of test is
this and can you support the company’s claim using the p-value?
Homework
Help:
6VC.
Determining when to reject or fail to reject, both methods (Links to an
external site.) (4:00)
6VE. Second
sample hypothesis testing from word problem to implications for claim, with
test statistic (Links to an external site.) (3:26)
6DD.
Determining when to reject or fail to reject, both methods (Links to an
external site.) (DOCX)
Claim is null, fail to reject the null and
support claim as the p-value (0.253) is greater than alpha (0.02)
Claim is null, reject the null and cannot
support claim as the p-value (0.253) is less than alpha (0.02)
Claim is alternative, reject the null and support
claim as the p-value (0.126) is greater than alpha (0.02)
Claim is alternative, fail to reject the null
and support claim as the p-value (0.126) is less than alpha (0.02)
Question 13A
business receives supplies of copper tubing where the supplier has said that
the average length is 26.70 inches so that they will fit into the business’
machines. A random sample of 48 copper tubes finds they have an average length
of 26.77 inches. The population standard deviation is assumed to be 0.20 inches.
At ?=0.05, should the business reject the supplier’s claim?
Homework
Help:
6VD. Sample
hypothesis testing from word problem to implications for claim, with p-values
(Links to an external site.) (3:15)
Yes, since p<?, we reject the null and the
null is the claim
No, since p>?, we fail to reject the null
and the null is the claim
Yes, since p>?, we fail to reject the null
and the null is the claim
No, since p>?, we reject the null and the
null is the claim
Question 14The
company’s cleaning service states that they spend more than 46 minutes each
time the cleaning service is there. The company times the length of 37 randomly
selected cleaning visits and finds the average is 46.5 minutes. Assuming a
population standard deviation of 5.2 minutes, can the company support the cleaning
service’s claim at ?=0.10?
Homework
Help:
6VD. Sample
hypothesis testing from word problem to implications for claim, with p-values
(Links to an external site.) (3:15)
Yes,
since p<?, we fail to reject the null. The claim is the null, so the claim
is not supported
Yes, since p<?, we reject the null. The
claim is the null, so the claim is not supported
No, since p<?, we reject the null. The
claim is the alternative, so the claim is supported
No, since p>?, we fail to reject the null.
The claim is the alternative, so the claim is not supported
Question 15A
customer service phone line claims that the wait times before a call is
answered by a service representative is less than 3.3 minutes. In a random
sample of 62 calls, the average wait time before a representative answers is
3.26 minutes. The population standard deviation is assumed to be 0.29 minutes.
Can the claim be supported at ?=0.08?
Homework
Help:
6VE. Second
sample hypothesis testing from word problem to implications for claim, with
test statistic (Links to an external site.) (3:26)
No, since test statistic is not in the
rejection region defined by the critical value, reject the null. The claim is
the alternative, so the claim is not supported
Yes, since test statistic is in the rejection
region defined by the critical value, reject the null. The claim is the
alternative, so the claim is supported
No, since test statistic is not in the
rejection region defined by the critical value, fail to reject the null. The
claim is the alternative, so the claim is not supported
Yes, since test statistic is in the rejection
region defined by the critical value, fail to reject the null. The claim is the
alternative, so the claim is supported
Question 16In
a hypothesis test, the claim is ??40 while the sample of 27 has a mean of 41
and a sample standard deviation of 5.9 from a normally distributed data set. In
this hypothesis test, would a z test statistic be used or a t test statistic
and why?
Homework Help:
6DE. When
to use z and when to use t distribution (Links to an external site.) (DOCX)
t test statistic would be used as the
standard deviation is less than 10
z test statistic would be used as the
population standard deviation is known
t test statistic would be used as the data
are normally distributed with an unknown population standard deviation
z test statistic would be used as the mean is
greater than 30
Question 17A
university claims that the mean time professors are in their offices for
students is at least 6.5 hours each week. A random sample of eight professors
finds that the mean time in their offices is 6.2 hours each week. With a sample
standard deviation of 0.49 hours from a normally distributed data set, can the
university’s claim be supported at ?=0.05?
Homework
Help:
6VE. Second
sample hypothesis testing from word problem to implications for claim, with
test statistic (Links to an external site.) (3:26)
6VF. Third
sample hypothesis testing from word problem to implications for claim, with t
distribution, test statistic and p-value (Links to an external site.) (4:03)
6DE. When
to use z and when to use t distribution (Links to an external site.) (DOCX)
No, since the test statistic is in the
rejection region defined by the critical value, the null is rejected. The claim
is the null, so is not supported
No, since the test statistic is not in the
rejection region defined by the critical value, the null is rejected. The claim
is the null, so is not supported
Yes, since the test statistic is not in the
rejection region defined by the critical value, the null is not rejected. The
claim is the null, so is supported
Yes, since the test statistic is in the
rejection region defined by the critical value, the null is not rejected. The
claim is the null, so is supported
Question 18A
credit reporting agency claims that the mean credit card debt in a town is greater
than $3500. A random sample of the credit card debt of 28 residents in that
town has a mean credit card debt of $3590 and a standard deviation of $391. At
?=0.10, can the credit agency’s claim be supported, assuming this is a normally
distributed data set?
Homework
Help:
6VD. Sample
hypothesis testing from word problem to implications for claim, with p-values
(Links to an external site.) (3:15)
6VF. Third
sample hypothesis testing from word problem to implications for claim, with t
distribution, test statistic and p-value (Links to an external site.) (4:03)
6DE. When
to use z and when to use t distribution (Links to an external site.) (DOCX)
No, since p of 0.12 is greater than 0.10,
reject the null. Claim is null, so is not supported
Yes, since p-value of 0.12 is greater than
0.10, fail to reject the null. Claim is null, so is supported
Yes, since p-value of 0.12 is less than 0.55,
reject the null. Claim is alternative, so is supported
No, since p-value of 0.12 is greater than 0.10,
fail to reject the null. Claim is alternative, so is not supported
Question 19A
car company claims that its cars achieve an average gas mileage of at least 26
miles per gallon. A random sample of eight cars form this company have an
average gas mileage of 25.6 miles per gallon and a standard deviation of 1 mile
per gallon. At ?=0.06, can the company’s claim be supported, assuming this is a
normally distributed data set?
Homework
Help:
6VE. Second
sample hypothesis testing from word problem to implications for claim, with
test statistic (Links to an external site.) (3:26)
6VF. Third
sample hypothesis testing from word problem to implications for claim, with t
distribution, test statistic and p-value (Links to an external site.) (4:03)
6DE. When
to use z and when to use t distribution (Links to an external site.) (DOCX)
No, since the test statistic of -1.13 is
close to the critical value of -1.24, the null is not rejected. The claim is
the null, so is supported
No, since the test statistic of -1.13 is in
the rejection region defined by the critical value of -1.77, the null is
rejected. The claim is the null, so is not supported
Yes, since the test statistic of -1.13 is not
in the rejection region defined by the critical value of -1.77, the null is not
rejected. The claim is the null, so is supported
Yes, since the test statistic of -1.13 is not
in the rejection region defined by the critical value of -1.55, the null is
rejected. The claim is the null, so is supported
Question 20A researcher wants to determine if
extra homework problems help 8th grade students learn algebra. An 8th grade
class is divided into pairs and one student from each pair has extra homework
problems and the other in the pair does not. After 2 weeks, the entire class
takes an algebra test and the results of the two groups are compared. To be a
valid matched pair test, what should the researcher consider in creating the
two groups?
Homework
Help:
6DF. Paired
sample experiment structure requirements and assumptions (Links to an external
site.) (DOCX)
That each pair of students has similar ages
at the time of the testing
That the group without extra homework
problems receives different instruction
That each pair of students has similar IQs or
abilities in mathematics
That the group with the extra homework
problems has fewer after school activities