STT 200 Lecture 2
04/15/2014
Quiz 7
Name__________________________________
Signature_________________________
Section #_______________
Directions: The quiz contains 16 multiple choice questions. Each question will be worth 1 point so that total points for this quiz is 16. There
is only one correct answer per question. If you would like to get partial credit, show your work below the question where it is appropriate.
The formulas which may be needed for the quiz are given below.
1) How many tissues should a package of tissues contain? Researchers have determined that a person
uses an average of 41 tissues during a cold. Suppose a random sample of 10,000 people yielded the
1)
following data on the number of tissues used during a cold: x = 35, s = 18. Identify the null and
alternative hypothesis for a test to determine if the mean number of tissues used during a cold is less
than 41.
A) H0 : μ = 41 vs. Ha : μ < 41
B) H0 : μ > 41 vs. Ha : μ ≤ 41
C) H0 : μ = 41 vs. Ha : μ > 41
D) H0 : μ = 41 vs. Ha : μ ≠ 41
2) I want to test H0 : p = .4 vs. Ha : p ≠ .4 using a test of hypothesis. If I concluded that p is .4 when, in fact,
2)
the true value of p is not .4, then I have made a __________.
A) correct decision
B) Type I error
C) Type I and Type II error
D) Type II error
3) A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets
complaints that their bottles are not holding enough liquid. To test this claim, the bottling company
randomly samples 64 bottles and finds the average amount of liquid held by the bottles is 11.9155
ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test is 0.0655. State the
proper conclusion.
A) At α = 0.05, reject the null hypothesis.
B) At α = 0.05, fail to reject the null hypothesis.
C) At α = 0.025, reject the null hypothesis.
D) At α = 0.05, accept the null hypothesis.
3)
4) A small private college is interested in determining the percentage of its students who live off campus
and drive to class. Specifically, it was desired to determine if less than 20% of their current students
live off campus and drive to class. Suppose a sample of 108 students produced a test statistic of z =
-1.35. Find the p-value for the test of interest to the college.
A) p = 0.9115
B) p = 0.0885
C) p = 0.4115
D) p = 0.1770
4)
Work:
5) 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 only if the average time spent
on a delivery does not exceed 36 minutes. The owner has randomly selected 21 customers and
delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 36
minutes. What assumption is necessary for this test to be valid?
A) The sample mean delivery time must equal the population mean delivery time.
B) The population of delivery times must have a normal distribution.
C) None. The Central Limit Theorem makes any assumptions unnecessary.
D) The population variance must equal the population mean.
1
5)
6) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer.
The customer has been assured that the mean weight of these cartridges is in excess of the 13 ounces
printed on each cartridge. To check this claim, a sample of n = 21 cartridges are randomly selected
6)
from the shipment and carefully weighed. Summary statistics for the sample are: x = 13.11 ounces,
s = .21 ounce. To determine whether the supplier's claim is true, consider the test,
H0 : μ = 13 vs. Ha : μ > 13, where μ is the true mean weight of the cartridges. Calculate the value of the
test statistic.
A) z=11.000
B) t=2.400
C) z=0.524
D) t=1.100
Work:
7) Suppose a sample of n =15 had produced a test statistic of t = 2.285 to test H0 : μ = 30 vs. Ha : μ ≠ 30 .
What is the p-value for this statistic?
A) 0.01<p-value<0.025
C) 0.02<p-value<0.05
7)
B) 0.975<p-value <0.99
D) 0.95<p-value <0.98
Work:
8) A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their
patients. To test this claim against the alternative that the actual proportion is less than 90%, a random
sample of 100 doctors was chosen which resulted in 94 who indicate that they recommend this cough
syrup. The test statistic in this problem is approximately:
A) -1.33
B) 1.33
C) 1.83
D) 1.67
8)
Work:
9) A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their
patients. To test this claim against the alternative that the actual proportion is less than 90%, a random
sample of doctors was taken. Suppose the test statistic is z = -2.23. Can we conclude that H0 should be
9)
rejected at the a) α = .10, b) α = .05, and c) α = .01 level?
A) a) yes; b) yes; c) no
B) a) no; b) no; c) no
C) a) yes; b) yes; c) yes
D) a) no; b) no; c) yes
Work:
10) A small private college is interested in determining the percentage of its students who live off campus
and drive to class. Specifically, it was desired to determine if less than 20% of their current students
live off campus and drive to class. The college decided to take a random sample of 108 of their current
students to use in the analysis. Is the sample size of n = 108 large enough to use this inferential
procedure?
A) Yes, since the central limit theorem works whenever proportions are used
B) Yes, since both np and nq are greater than or equal to 10
C) Yes, since n ≥ 30
D) No
Work:
2
10)
11) Residuals for a linear regression model are . . .
A) variation in the data that is explained by the model.
B) data collected from individuals that is not consistent with the rest of the group.
C) the difference between observed responses and values predicted by the model.
D) possible models not explored by the researcher.
11)
12) Which scatterplot shows a strong association between two variables even though the correlation, r, is
probably near zero?
A)
B)
C)
D)
12)
13) The correlation between a family’s weekly income and the amount they spend on restaurant meals is
found to be r = 0.30. Which must be true?
I.
Families tend to spend about 30% of their incomes in restaurants.
II.
In general, the higher the income, the more the family spends in restaurants.
III.
The line of best fit passes through 30% of the (income, restaurant$) data points.
A) I, II, and III
B) I only
C) II only
D) II and III only
13)
14) The regression analysis below examines the relationship between the number of years of formal
education a person has and their annual income. According to this model, about how much more
money do people who finish a 4-year college program earn each year, on average, than those with
only a 2-year degree?
14)
A) $5337
B) $2006
C) $7968
D) $2710
Work:
15) A county real estate appraiser wants to develop a statistical model to predict the appraised value of
houses in a section of the county called East Meadow. One of the many variables thought to be an
important predictor of appraised value is the number of rooms in the house. Consequently, the
appraiser decided to fit the simple linear regression model:
^
y = b0 + b1 x,
where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data
collected for a sample of n = 74 houses in East Meadow, the following results were obtained:
^
y = 74.80 + 19.79x
Give a practical interpretation of the estimate of the slope of the least squares line.
A) For each additional dollar of appraised value, we estimate the number of rooms in the house to
increase by 19.79.
B) For a house with 0 rooms, we estimate the appraised value to be $74,800.
C) For each additional room in the house, we estimate the appraised value to increase $74,800 on
average.
D) For each additional room in the house, we estimate the appraised value to increase $19,790 on
average.
3
15)
16) A large national bank charges local companies for using its services. A bank official reported the
results of a regression analysis designed to predict the bank's charges (y), measured in dollars per
month, for services rendered to local companies. One independent variable used to predict the service
charge to a company is the company's sales revenue (x), measured in $ million. Data for 21 companies
who use the bank's services were used to fit the model
E(y) = β0 + β1 x.
The results of the simple linear regression are provided below.
^
y = 2,700 + 20x
Interpret the estimate of β0 , the y-intercept of the line.
A) All companies will be charged at least $2,700 by the bank.
B) About 95% of the observed service charges fall within $2,700 of the least squares line.
C) For every $1 million increase in sales revenue, we expect a service charge to increase $2,700.
D) There is no practical interpretation since a sales revenue of $0 is a nonsensical value.
4
16)
Answer Key
Testname: STT200_QUIZ 7_SOLUTIONS
1) A
2) D
3) B
4) B
5) B
6) B
7) C
8) B
9) A
10) B
11) C
12) A
13) C
14) A
15) D
16) D
5