MATH221 Statistics for Decision Making
Week 7 Quiz
Question 1(CO
4) From a random sample of 55 businesses, it is found that the mean time that
employees spend on personal issues each week is 4.9 hours with a standard
deviation of 0.35 hours. What is the 95% confidence interval for the amount of
time spent on personal issues?
(4.81, 4.99)
(4.84, 4.96)
(4.83, 4.97)
(4.82, 4.98)
Question 2(CO
4)If a confidence interval is given from 8.50 to 10.25 and the mean is known to
be 9.375, what is the margin of error?
1.750
0.875
8.500
0.438
Question 3(CO
4) If the population standard deviation of a increases without other changes,
what is most likely to happen to the confidence interval?
does not change
widens
cannot determine
narrows
Question 4(CO
4) From a random sample of 41 teens, it is found that on average they spend
43.1 hours each week online with a population standard deviation of 5.91 hours.
What is the 90% confidence interval for the amount of time they spend online
each week?
(37.19, 49.01)
(40.58, 45.62)
(31.28, 54.92)
(41.58, 44.62)
Question 5(CO
4) A company making refrigerators strives for the internal temperature to have
a mean of 37.5 degrees with a population standard deviation of 0.6 degrees,
based on samples of 100. A sample of 100 refrigerators have an average
temperature of 37.48 degrees. Are the refrigerators within the 90% confidence
interval?
Yes, the temperature is within the confidence
interval of (37.40, 37.60)
Yes, the temperature is within the confidence
interval of (36.90, 38.10)
No, the temperature is outside the confidence
interval of (36.90, 38.10)
No, the temperature is outside the confidence
interval of (37.40, 37.60)
Question 6(CO
4) What is the 97% confidence interval for a sample of 104 soda cans that have
a mean amount of 15.10 ounces and a population standard deviation of 0.08
ounces?
(15.940, 15.260)
(15.083, 15.117)
(12.033, 12.067)
(15.020, 15.180)
Question 7(CO
4) Determine the minimum sample size required when you want to be 98% confident
that the sample mean is within two units of the population mean. Assume a
population standard deviation of 5.75 in a normally distributed population.
45
23
43
44
Question 8(CO
4) Determine the minimum sample size required when you want to be 80% confident
that the sample mean is within 1.5 units of the population mean. Assume a
population standard deviation of 9.24 in a normally distributed population.
62
146
145
63
Question 9(CO
4) Determine the minimum sample size required when you want to be 75% confident
that the sample mean is within thirty units of the population mean. Assume a
population standard deviation of 327.8 in a normally distributed population
158
324
197
157
Question 10(CO
4) In a sample of 8 high school students, they spent an average of 28.8 hours
each week doing sports with a sample standard deviation of 3.2 hours. Find the
95% confidence interval, assuming the times are normally distributed.
(25.62, 32.48)
(24.10, 34.50)
(26.12, 31.48)
(22.47, 35.21)
Question 11(CO
4) In a sample of 15 stuffed animals, you find that they weigh an average of
8.56 ounces with a sample standard deviation of 0.08 ounces. Find the 92%
confidence interval, assuming the times are normally distributed.
(8.521, 8.599)
(8.528, 8.591)
(8.543, 8.577)
(8.516, 8.604)
Question 12(CO
4) Market research indicates that a new product has the potential to make the
company an additional $3.8 million, with a standard deviation of $1.9 million.
If this estimate was based on a sample of 10 customers from a normally
distributed data set, what would be the 90% confidence interval?
(2.00, 5.60)
(2.51, 5.09)
(1.90, 5.71)
(2.70, 4.90)
Question 13
(CO 4) Supplier claims that they are 95% confident that their products will be
in the interval of 20.45 to 21.05. You take samples and find that the 95%
confidence interval of what they are sending is 20.40 to 21.00. What conclusion
can be made?
The supplier products have a higher mean than
claimed
The supplier is less accurate than they have
claimed
The supplier products have a lower mean than
claimed
The supplier is more accurate than they
claimed
Question
14(CO 4) In a sample of 17 small candles, the weight is found to be 3.72 ounces
with a standard deviation of 0.963 ounces. What would be the 87% confidence
interval for the size of the candles, assuming the data are normally
distributed?
(2.757, 4.683)
(3.369, 4.071)
(3.347, 4.093)
(3.199, 4.241)
Question
15(CO 4) In a situation where the sample size was decreased from 39 to 29 in a
normally distributed data set, what would be the impact on the confidence
interval?
It would become narrower with fewer values
It would remain the same as sample size does
not impact confidence intervals
It would become narrower due to using the z
distribution
It would become wider with fewer values
Question
16(CO 5) A company claims that its heaters last more than 5 years. Write the
null and alternative hypotheses and note which is the claim.
Ho: ? ? 5, Ha: ? < 5 (claim)
Ho: ? = 5 (claim), Ha: ? ? 5
Ho: ? > 5 (claim), Ha: ? ? 5
Ho: ? ? 5, Ha: ? > 5 (claim)
Question
17(CO 5) An executive claims that her employees spend no less than 2.5 hours
each week in meetings. Write the null and alternative hypotheses and note which
is the claim.
Ho: ? = 2.5, Ha: ? ? 2.5 (claim)
Ho: ? > 2.5, Ha: ? ? 2.5 (claim)
Ho: ? ? 2.5 (claim), Ha: ? < 2.5
Ho: ? ? 2.5 (claim), Ha: ? > 2.5
Question
18(CO 5) In hypothesis testing, a key element in the structure of the
hypotheses is that the math tests the support for the ________________________.
the truth
null hypothesis
claim
alternative hypothesis
Question 19
(CO 5) A landscaping company claims that at most 90% of workers arrive on time.
If a hypothesis test is performed that rejects the null hypothesis, how would
this decision be interpreted?
There is sufficient evidence to support the
claim that at most 90% of workers arrive on time
There is not sufficient evidence to support the
claim that at most 90% of workers arrive on time
There is not sufficient evidence to support
the claim that at least 90% of workers arrive on time
There is sufficient evidence to support the
claim that a least 90% of workers arrive on time
Question 20
(CO 5) A textbook company claims that their book is so engaging that less than
55% of students read it. If a hypothesis test is performed that rejects the
null hypothesis, how would this decision be interpreted?
There is not sufficient evidence to support
the claim that less than 55% of students read this text
There is sufficient evidence to support the
claim that no more than 55% of students read this text
There is not sufficient evidence to support
the claim that no more than 55% of students read this text
There is sufficient evidence to support the
claim that less than 55% of students read this text
Question
21(CO 5) An advocacy group claims that the mean braking distance of a certain
type of tire is 75 feet when the car is going 40 miles per hour. In a test of
80 of these tires, the braking distance has a mean of 77 and a population
standard deviation of 5.9 feet. Find the standardized test statistic and the
corresponding p-value.
z-test statistic = 3.03, p-value = 0.0012
z-test statistic = -3.03, p-value = 0.0024
z-test statistic = 3.03, p-value = 0.0024
z-test statistic = -3.03, p-value = 0.0012
Question
22(CO 5) The heights of 82 roller coasters have a mean of 280.7 feet and a
population standard deviation of 59.3 feet. Find the standardized tests
statistics and the corresponding p-value when the claim is that roller coasters
are more than 290 feet tall.
z-test statistic = 1.42, p-value = 0.1556
z-test statistic = 1.42, p-value = 0.0778
z-test statistic = -1.42, p-value = 0.0778
z-test statistic = -1.42, p-value = 0.1556
Question 23
(CO 5) A light bulb manufacturer guarantees that the mean life of a certain
type of light bulb is at least 720 hours. A random sample of 51 light bulbs as
a mean of 701.6 hours with a population standard deviation of 62 hours. At an
?=0.05, can you support the company’s claim using the test statistic?
Claim is the null, fail to reject the null
and cannot support claim as test statistic (-2.12) is not in the rejection
region defined by the critical value (-1.645)
Claim is the alternative, fail to reject the
null and cannot support claim as the test statistic (-2.12) is in the rejection
region defined by the critical value (-1.96)
Claim is the null, reject the null and cannot
support claim as test statistic (-2.12) is in the rejection region defined by
the critical value (-1.645)
Claim is the alternative, reject the null and
support claim as test statistic (-2.12) is not in the rejection region defined
by the critical value (-1.96)
Question
24(CO 5) A restaurant claims the customers receive their food in less than 16
minutes. A random sample of 39 customers finds a mean wait time for food to be
15.8 minutes with a population standard deviation of 1.4 minutes. At ? = 0.04,
can you support the organizations’ claim using the test statistic?
Claim is the alternative, reject the null so
support the claim as test statistic (-0.89) is in the rejection region defined
by the critical value (-2.05)
Claim is the alternative, fail to reject the
null so cannot support the claim as test statistic (-0.89) is not in the
rejection region defined by the critical value (-1.75)
Claim is the null, reject the null so cannot
support the claim as test statistic (-0.89) is in the rejection region defined by
the critical value (-2.05)
Claim is the null, fail to reject the null so
support the claim as test statistic (-0.89) is not in the rejection region
defined by the critical value (-1.75)
Question 25
(CO 5) A manufacturer claims that their calculators are 6.800 inches long. A
random sample of 55 of their calculators finds they have a mean of 6.812 inches
with a population standard deviation of 0.05 inches. At ?=0.08, can you support
the manufacturer’s claim using the p value?
Claim is the alternative, fail to reject the
null and support claim as p-value (0.075) is less than alpha (0.08)
Claim is the null, reject the null and cannot
support claim as p-value (0.075) is less than alpha (0.08)
Claim is the alternative, reject the null and
cannot support claim as p-value (0.038) is greater than alpha (0.08)
Claim is the null, fail to reject the null
and support claim as p-value (0.038) is greater than alpha (0.08)
Question
26(CO 5) A travel analyst claims that the mean room rates at a three-star hotel
in Chicago is greater than $152. In a random sample of 36 three-star hotel
rooms in Chicago, the mean room rate is $163 with a population standard
deviation of $41. At ?=0.10, can you support the analyst’s claim using the
p-value?
Claim is the null, fail to reject the null as
p-value (0.054) is less than alpha (0.10), and cannot support the claim
Claim is the alternative, fail to reject the
null as p-value (0.054) is less than alpha (0.10), and can support the claim
Claim is the alternative, reject the null as
p-value (0.054) is less than alpha (0.10), and can support the claim
Claim is the null, reject the null as p-value
(0.054) is less than alpha (0.10), and cannot support the claim
Question
27(CO 5) A car company claims that the mean gas mileage for its luxury sedan is
at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage
of 23 miles per gallon and a standard deviation of 2.4 miles per gallon. At
?=0.05, can you support the company’s claim assuming the population is normally
distributed?
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 not rejected. The
claim is the null, so is 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 alternative, so is 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
Question
28(CO 5) A state Department of Transportation claims that the mean wait time
for various services at its different location is more than 6 minutes. A random
sample of 16 services at different locations has a mean wait time of 9.5
minutes and a standard deviation of 7.3 minutes. At ?=0.05, can the
department’s claim be supported assuming the population is normally
distributed?
Yes, since p of 0.037 is less than 0.05, fail
to reject the null. Claim is null, so is supported
Yes, since p of 0.037 is less than 0.05,
reject the null. Claim is alternative, so is supported
No, since p of 0.037 is less than 0.05, reject
the null. Claim is null, so is not supported
No, since p of 0.037 is less than 0.05, fail
to reject the null. Claim is alternative, so is not supported
Question 29
(CO 5) A used car dealer says that the mean price of a three-year-old sport
utility vehicle in good condition is $18,000. A random sample of 20 such
vehicles has a mean price of $18,450 and a standard deviation of $1930. At
?=0.08, can the dealer’s claim be supported assuming the population is normally
distributed?
Yes, since the test statistic of 1.04 is not
in the rejection region defined by the critical value of 1.85, the null is not
rejected. The claim is the null, so is supported
No, since the test statistic of 1.04 is in
the rejection region defined by the critical value of 1.85, the null is
rejected. The claim is the null, so is not supported
No, since the test statistic of 1.04 is close
to the critical value of 1.24, the null is not rejected. The claim is the null,
so is supported
Yes, since the test statistic of 1.04 is in the
rejection region defined by the critical value of 1.46, the null is rejected.
The claim is the null, so is supported
Question
30(CO 5) A researcher wants to determine if daily talks together strengthen a
marriage. One group of wives and one group of husbands are selected and have
daily talks. After 2 weeks, all are asked if they felt their marriage was
stronger based on the talks 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?
That the both groups were positive on
marriage before the walks
That the husbands and wives selected were
married to each other
That all husbands and wives in the test had
been married about the same amount of time
That the wives group was positive on marriage
before the walks