Question

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: μ ≤ 63, Ha: μ < 63 (claim) Ho: μ = 63
(claim), Ha: μ ≥ 63 Ho: μ ≤ 63, Ha: μ > 63 (claim)

Ho: μ > 63 (claim), Ha: μ ≤ 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: μ > 5.9 (claim), Ha: μ > 5.9

Ho: μ ≥ 5.9, Ha: μ ≤ 5.9 (claim)

Ho: μ ≤ 5.9 (claim), Ha: μ > 5.9

Ho: μ > 5.9, Ha: μ ≤ 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: μ > 20000 (claim), Ha: μ = 20000

Ho: μ ≤ 20000, Ha: μ > 20000 (claim)

Ho: μ ≥ 20000 (claim), Ha: μ < 20000 Ho: μ =
20000, Ha: μ ≤ 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: μ > 23, Ha: μ ≤ 23 (claim)

Ho: μ ≠ 23, Ha: μ = 23 (claim)

Ho: μ = 23 (claim), Ha: μ ≠ 23

Ho: μ = 23 (claim), Ha: μ ≤ 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 α=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 α=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 α=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 α=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 pα, we fail to reject the null and the null
is the claim

Yes, since p>α, we fail to reject the null and the
null is the claim

No, since p>α, 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 α=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 pα, 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 α=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 μ≤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 α=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
α=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 α=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

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