FLORIDA UNIVERSITY DEPARTMENT OF STATISTICS
STA6126 TEST – 2 FALL 2011
Please sign the following:
NAME: UFID: Signature:

Tables and Formulas are at the end of the test.

You may use one sheet (2 pages) of your notes.

Choose the best answer and fill the corresponding bubble.
1.
Suppose the proportion of students retained in 2003 is p
03
and the proportion of students retained in 2004 is p
04
. A 90% confidence interval for p
03
– p
04
is (-0.0398, 0.0262). Give an interpretation of this confidence interval.
A) We are confident that 90% of students retained in 2004 between 3.98% less and
2.62% more than 2003.
B) We know that 90% of all random samples done on the population will show that the proportion of students retained in 2003 is between 3.98% less and 2.62% more than the proportion of students retained in 2004.
C) We are 90% confident that the proportion of students retained in 2003 is between 3.98% less and 2.62% more than the proportion of students retained in
2004.
D) We know that 90% of students retained in 2003 between 3.98% less and 2.62% more than 2004.
E) We are 90% confident that the proportion of students retained in 2004 is between
3.98% less and 2.62% more than the proportion of students retained in 2003.
2.
A survey of shoppers is planned to see what percentage use credit cards. Prior surveys suggest 63% of shoppers use credit cards. How many randomly selected shoppers must we survey in order to estimate the proportion of shoppers who use credit cards to within 4% with
95% confidence?
A) 432
B) 560
C) 1513
D) 504
E) 967
3.
Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions described below, which table should you use?
Conditions: The population standard deviation is unknown, the data contain outliers and the sample size is small.
A) Z-Table B) T-Table C) Either D) Neither
4.
A significance test is used to prevent a machine from under-filling or over-filling quart bottles of beer. On the basis of sample, the null hypothesis is rejected and the machine is shut down for inspection. A thorough examination reveals there is nothing wrong with the filling machine.
From a statistical point of view:
A) Both Type I and Type II errors were made. B) A Type II error was made.
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C) A Type I error was made. made.
D) A correct decision was
E) The machine should be under warrantee.
5.
A community college wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluates its retention rate and comes up with a p-value of 0.075. What is reasonable to conclude about the new programs?
A) There is a 7.5% chance of the new programs having no effect on retention.
B) There's only a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective.
C) We can say there is a 7.5% chance of seeing the new programs having an effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective.
D) We can say there is a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. There is no evidence the new programs are more effective, but we cannot conclude the new programs have no effect on retention.
E) There is a 92.5% chance of the new programs having no effect on retention.
6.
In monitoring lead in the air after an explosion at a battery factory, it is found that measured the amounts of lead (in ug/m3) in a 6 days period had a standard error of 1.91.
Find the margin of error that corresponds to a 95% confidence interval.
A) 1.91
B) 5.65
C) 95
D) 3.74
E) None of the above.
7.
A researcher collected data on the annual salary of doctors in Illinois. He wishes to construct a confidence interval for the mean annual salary. Which of the following are true?
I. A 98% confidence interval will have a greater chance of including the true mean salary than a 95% confidence interval.
II. A 98% confidence interval will be narrower than a 95% confidence interval.
III. A 98% confidence interval requires the researcher to take a larger sample.
A) I and II B) III only C) I only D) II only E) II and III
8.
Data were collected from CEO's in the consumer products and telecommunication industries.
It is desired to compare the mean salaries between CEO's in the consumer products industry and CEO's in the telecommunications industry. The data were analyzed using a software package giving the following output. Find the p-value.
Ho: μ
X
= μ
Y
vs. Ha: μ
X
≠ μ
Y
Samples from SALARY
X = Consumer Products Y = Telecommunications
X
Y
X
= 1761
= 1093.5

Y = 667.5
S
X
= 397.555 n
X
= 21
S
Y
= 103.255 n
Y
= 21
2

T cal
= 1.47809
A) p-value = 0.9262 B) p-value = 0.29525 C) p-value = 1.47809
D) 0.05 < p-value < 0.10 E) 0.10 < p-value < 0.20
9.
A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 25 minutes. The owner has randomly selected 18 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 25 minutes.
Which one of the following assumptions is necessary for this test to be valid?
A) The population of delivery times must have a binomial distribution.
B) The population of delivery times must have a normal distribution.
C) None. The Central Limit Theorem makes any assumptions unnecessary.
D) The sample mean delivery time must equal the population mean delivery time.
E) The population variance must equal the population mean.
10.
A survey was conducted to determine the difference in gasoline mileage for two types of trucks. A random sample was taken for each model of truck, and the mean gasoline mileage, in miles per gallon, was calculated. A 98% confidence interval for the difference in the mean mileage for model A trucks and the mean mileage for model B trucks, μ
A
– μ
B
was determined to be (2.5, 4.7). Interpret the confidence interval.
A) Based on this sample, we are 98% confident that the average mileage for model B trucks is between 2.5 and 4.7 miles per gallon higher than the average mileage for model A trucks.
B ) Based on this sample, we are 98% confident that the average mileage for model
A trucks is between 2.5 and 4.7 miles per gallon higher than the average mileage for model B trucks.
C) We are 98% confident that a randomly selected model A truck will get mileage that is between 2.5 and 4.7 miles per gallon higher than a randomly selected model B truck.
D) We know that 98% of all random samples done on the population of trucks will show that the average mileage for model A trucks is between 2.5 and 4.7 miles per gallon higher than the average mileage for model B trucks.
E) We know that 98% of model A trucks get mileage that is between 2.5 and 4.7 miles per gallon higher than model B trucks.
11.
A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. The following are observed from two independent random samples. Find the value of the test statistic for testing the claim that the treatment is effective.
Sample size
Sample
Mean
Standard
Deviation
Treatment
Control
85
75
189.1
203.7
38.7
39.2
A) Z cal
= – 2.367
B) T cal
= – 0.096
C) T cal
= – 2.367
3

D) Z cal
= – 0.952
E) T cal
= – 0.952
12.
The real estate industry claims that it is the best and most effective system to market residential real estate. A survey of randomly selected home sellers in Illinois found that a
95% confidence interval for the proportion of homes that are sold by a real estate agent is
69% to 81%. Interpret the interval in this context
A) 95% of all random samples of home sellers in Illinois will show that between 69% and
81% of homes are sold by a real estate agent.
B) We are 95% confident that between 69% and 81% of homes in this survey are sold by a real estate agent.
C) 95% of all homes in Illinois are sold by a real estate agent.
D) In 95% of the years, between 69% and 81% of homes in Illinois are sold by a real estate agent.
E) We are 95% confident, based on this sample, that between 69% and 81% of all homes in Illinois are sold by a real estate agent.
13.
Which of the following statements about the t distribution is true?
A) It has less area in the tails than does the normal distribution.
B) It assumes the population is normally distributed.
C) It is used to construct confidence intervals for the population mean when the population standard deviation is known.
D) It approaches the normal distribution as the sample size decreases.
E) It assumes the population is not normally distributed.
14.
What factor or factors affect the choice of the sample size when estimating μ or p?
A) confidence level B) variability in the data C) desired precision
D) financial cost E) All of the above.
15.
Fill in the blank: Both the sample mean and the sample proportion are ______________ of the population mean and the population proportion, respectively.
A) point estimates B) interval estimates C) unbiased estimates
D) biased estimates
16.
The sampling distribution of
E) Both A and C
ˆ p
1
 ˆ p
2 is approximately normal when
A) n
1
= n
2
= 50, p
1
= 0.10 and p
2
= 0.02.
B) n
1
= n
2
= 100, p
1
= 0.15 and p
2
= 0.17.
C) n
1
≥ 30 and n
2
≥ 30.
D) n
1
= n
2
= 20, p
1
= 0.70 and p
2
= 0.17.
E) n
1
= n
2
= 100, p
1
= 0.06 and p
2
= 0.17.
17.
Which of the following is a misinterpretation of the results of a significance test?
A) concluding that the probability that Ho is true is equal to the P-value
B) deciding to reject Ho because the p-value is ≤ α.
C) deciding to fail to reject Ho because the p-value is larger than α
D) concluding that a p-value ≤ α implies a statistically significant result
E) None of the above.
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18.
In a survey of 500 residents, 300 were opposed to the use of the photo-cop for issuing traffic tickets. The standard error of the proportion is found to be 0.022. Find the margin of error that corresponds to a 95% confidence interval.
A) 0.035 B) 0.60
E) None of the above.
C) 0.043
D) 0.40
19.
Analysis of a random sample of 250 Virginia nurses produced a 95% confidence interval for the mean annual salary of ($42,838 , $49,691). Interpret the confidence interval.
A) About 95% of the nurses surveyed earn between $42,838 and $49,691.
B) If we took many random samples of Virginia nurses, about 95% of them would produce this confidence interval.
C) About 95% of Virginia nurses earn between $42,838 and $49,691.
D) 95% of all nurses earn between $42,838 and $49,691.
E) We are 95% confident that the interval from $42,838 to $49,691 contains the true mean salary of all Virginia nurses.
20.
A claim is made that the proportion of children who play sports is less than 50%. A random sample of 1933 subjects had 30% saying that they play a sport.
Find the calculated value of the test statistic.
A) Z cal
= 35.90
B) Z
cal
= 17.59
C) Z
cal
= - 17.59
D) T
cal
= - 35.90
E) T
cal
= 0.50
21.
Scores on a certain test are normally distributed with a variance of 14. A researcher wishes to estimate the mean score achieved by all adults on the test.
Find the sample size needed to assure with 98% confidence that the sample mean will not differ from the population mean by more than 2 units.
A) 11
B) 20
C) 400
D) 267
E) 39
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Parameter Estimator


X
 
1

 d
=
2
(Dependent
Samples)
 
1

2
(Independent
Samples)

1
2
 
2
2
(unknown)
 
1

2
(Independent
Samples)

1
2
 
2
2
(unknown)
 
1

2
(Independent
Samples)
X
ˆp
X d
Some formulae you may need
SE(Estimator) or its estimate

X
S /
/ n n or
Z
T
 and its distribution
X

0


X
/ n

X
Test Statistic
 
0
S / n
~ t
( n

1 )
For CI:
For tests:
ˆ p( 1
 ˆ p ) n

0
( 1
 
0
) n
Z
 p
 
0

0
( 1
 
0 n
)
S / n T

X d
 
0
S / n
~ t
( n

1 )
X
1

X
2
X
1

X
2
ˆ p
 p
1
ˆ
2
S pooled
S
1
2

S n n
1 2
2
2

1
1
 n n
1
2
T
T

( X
1

X )
2


S
1
2

S n n
1 2
2

2



0 ~ t
( df )
 df = min of {(n
1
–1), (n
2
–1)}
( X
1

X )
2




S pooled

1 n n
1


0
1
2



~ t
( df ) df = (n
1
+ n
2
–2) n
For CI:
ˆ p (
1
1
 ˆ p )
1

ˆ p (
2
1
 ˆ p )
2 n
1 n
2 se
0

S pooled
For Tests:
ˆ p( 1
 ˆ p )


1

1 n n
1 2



( n
1

1 )S
1
2 
( n
2

1 )S
( n
1
 
2

1 )
2
2
 
2
 z

B
/ 2
 2
Z

ˆ p n
 p( 1
 p )
 z

B
/ 2
 2
1
 se
0
ˆ p
2
6