Assignment 4, due on Nov. 23 at 5:00pm
Name___________________________________
Student Number:
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent
agency recently was asked to investigate this question. The agency randomly selected 100 items
common to each of two supermarkets (labeled A and B) and recorded the prices charged by each
supermarket. The summary results are provided below:
x A = 2.09
x B = 1.99
sA = 0.22
sB = 0.19
d = .10
sd = .03
Assuming a matched pairs design, which of the following assumptions is necessary for a
confidence interval for the mean difference to be valid?
A) The samples are randomly and independently selected.
B) None of these assumptions are necessary.
C) The population of paired differences has an approximate normal distribution.
D) The population variances must be equal.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
2) The data for a random sample of five paired observations are shown below.
Pair Observation 1
1
3
2
4
3
3
4
2
5
5
a.
2)
Observation 2
5
4
4
5
6
Calculate the difference between each pair of observations by subtracting observation
2 from observation 1. Use the differences to calculate d and sd .
b.
c.
Calculate the means x 1 and x 2 of each column of observations. Show that d = x 1 - x 2 .
Form a 90% confidence interval for µD.
3) A paired difference experiment produced the following results.
nd = 40, x 1 = 18.4, x2 = 19.7, d = -1.3, sd2 = 5
Perform the appropriate test to determine whether there is sufficient evidence to conclude
that µ1 < µ2 using = .10.
1
3)
1)
4) One indication of how strong the real estate market is performing is the proportion of
properties that sell in less than 30 days after being listed. Of the condominiums in a Florida
beach community that sold in the first six months of 2006, 75 of the 115 sampled had been
on the market less than 30 days. For the first six months of 2007, 25 of the 85 sampled had
been on the market less than 30 days. Test the hypothesis that the proportion of
condominiums that sold within 30 days decreased from 2006 to 2007. Use = .01.
4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
5) The FDA is comparing the mean caffeine contents of two brands of cola. Independent random
samples of 6-oz. cans of each brand were selected and the caffeine content of each can determined.
The study provided the following summary information.
Sample size
Mean
Variance
Brand A
15
18
1.2
5)
Brand B
10
20
1.5
How many cans of each soda would need to be sampled in order to estimate the difference in the
mean caffeine content to within .5 with 95% reliability?
A) n1 = n2 = 21
B) n1 = n2 = 57
C) n1 = n2 = 42
D) n1 = n2 = 18
6) A consumer protection agency is comparing the work of two electrical contractors. The agency
plans to inspect residences in which each of these contractors has done the wiring in order to
estimate the difference in the proportions of residences that are electrically deficient. Suppose the
proportions of residences with deficient work are expected to be about .7 for both contractors. How
many homes should be sampled in order to estimate the difference in proportions using a 95%
confidence interval of width .3?
A) n1 = n2 = 72
B) n1 = n 2 = 144
C) n1 = n2 = 36
D) n1 = n2 = 240
6)
7) A random sample of n observations, selected from a normal population, is used to test the null
hypothesis H0 : 2 = 155. Specify the appropriate rejection region.
Ha : 2 155, n = 10, = .05
A) 2 < 3.24697 or 2 > 20.4831
B) 2.70039 < 2 < 19.0228
7)
C) 2 < 2.70039 or 2 > 19.0228
D) 2 < 3.32511 or 2 > 16.9190
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
8) An educational testing service designed an achievement test so that the range in student
scores would be greater than 420 points. To determine whether the objective was achieved,
the testing service gave the test to a random sample of 30 students and found that the
sample mean and variance were 759 and 1943, respectively. Conduct the test for
H0 : 2 = 4900 vs. Ha : 2 > 4900 using = .025. Assume the range is 6 .
8)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
9) Find F.05 where v 1 = 8 and v 2 = 11.
A) 3.66
B) 4.74
9)
C) 2.30
2
D) 2.95
Specify the appropriate rejection region for testing H0 :
10) Ha :
2
1
2
2;
2
1 =
2
2 in the given situation.
= 0.10, n 1 = 10, n 2 = 16
10)
2
2
Assume that s 2 > s 1 .
A) F > 2.34
B) F > 3.01
C) F > 2.59
3
D) F > 2.59
Answer Key
Testname: ASSIGNMENT_4
1) B
2) a.
The differences are 2, 0, 1, 3, and 1; d = -1.4; sd = 1.14
b.
x 1 = 3.4, x 2 = 4.8, x 1 - x 2 = 3.4 - 4.8 = - 1.4 = d
c.
-1.4 ± 2.132
1.14
5
3) The test statistic is z =
-1.4 ± 1.09
-1.3 - 0
5 / 40
-3.677.
The rejection region is z < -1.28.
Since the test statistic does fall in the rejection region, we have sufficient evidence to conclude that µ1 < µ2.
^
^
(.65 - .29) - 0
5.43.
4) p 1 .65 and p 2 = .29; The test statistic is z =
.65(.35) .29(.71)
+
115
85
The rejection region is z > 2.33. Since the test statistic falls in the rejection region, we reject the null hypothesis in favor
of the alternative hypothesis that (p 1 - p 2 ) > 0. We conclude that the proportion of condominiums that sold within 30
days was greater in the first half of 2006 than in the first half of 2007.
5) C
6) A
7) C
8) We test H0 : 2 = 4900
Ha : 2 > 4900
(n -1)s2 (30 -1)1943
The test statistic is X2 =
=
= 11.499
2
4900
The rejection region requires
= .025 in the upper tail of the X2 distribution with n - 1 = 30 - 1 = 29 df. So X2 .025 =
45.722. The rejection region is X2 > 45.722.
Since the observed value of the test statistic does not fall in the rejection region (X2 = 11.499 45.722), H0 cannot be
rejected. There is insufficient evidence to indicate the variance is greater than 4900 at
9) D
10) B
4
= .025.