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Question 1
Exercise 12-2
Consider a multinomial experiment with n = 340 and k = 3. The null hypothesis is H0: p1 = 0.60, p2 = 0.25, and p3
= 0.15. The observed frequencies resulting from the experiment are:
Category 1 2 3
Frequency 230 80 30
________________________________________
(Use Table 3)
a. Choose the appropriate alternative hypothesis.
All population proportions differ from their hypothesized values.
At least one of the population proportions differs from its hypothesized value.
b-1. Calculate the value of the test statistic.(Round intermediate calculations to 4 decimal places and your final
answer to 2 decimal places.)
Test statistic
b-2. Approximate the p-value.
0.025 < p-value < 0.050
p-value < 0.005
0.005 < p-value < 0.010
0.010 < p-value < 0.025
0.050 < p-value < 0.100
c. At the 1% significance level, what is the conclusion to the hypothesis test?
Do not reject H0 since the p-value is more than α.
Reject H0 since the p-value is less than α.
Reject H0 since the p-value is more than α.
Do not reject H0 since the p-value is less than α.
Question 3
Exercise 13-1
A random sample of five observations from three treatments produced the following data: Use Table 4.
Treatments
A B C
22 24 26
30 30 23
29 16 18
21 20 22
26 25 16
= 25.6 = 23.0 = 21.0
sA2 = 16.3 sB2 = 28.0 sC2 = 16.0
________________________________________
a. Calculate the grand mean. (Round your answer to 2 decimal places.)
Grand mean
b. Calculate SSTR and MSTR. (Round intermediate values to 4 decimal places and final answers to 2 decimal
places.)
SSTR
MSTR
________________________________________
c. Calculate SSE and MSE. (Round intermediate values to 4 decimal places and final answers to 2 decimal places.)
SSE
MSE
________________________________________
d. Specify the competing hypotheses in order to determine whether some differences exist between the population
means.
H0: μA ≤ μB ≤ μC; HA: Not all population means are equal.
H0: μA ≥ μB ≥ μC; HA: Not all population means are equal.
H0: μA = μB = μC; HA: Not all population means are equal.
e. Calculate the value of the F(df1,df2) test statistic. (Do not round intermediate calculations. Round your answer to
2 decimal places.)
Test statistic
f. Using the critical value approach at the 1% significance level, what is the conclusion to the test?
Reject H0 since the value of the test statistic exceeds 6.93.
Reject H0 since the value of the test statistic exceeds 5.52.
Do not reject H0 since the value of the test statistic does not exceed 5.52.
Do not reject H0 since the value of the test statistic does not exceed 6.93.
Question 5
Exercise 12-17
The following sample data reflect shipments received by a large firm from three different vendors.
Use Table 3.
Vendor Defective Acceptable
1 16 132
2 14 78
3 25 233
________________________________________
a. Choose the competing hypotheses to determine whether quality is associated with the source of the shipments.
H0: Quality and source of shipment (vendor) are dependent.; HA: Quality and source of shipment (vendor) are
independent.
H0: Quality and source of shipment (vendor) are independent.; HA: Quality and source of shipment (vendor) are
dependent.
b-1. Calculate the value of the test statistic.(Round intermediate calculations to 4 decimal places and your final
answer to 2 decimal places.)
χ2df
b-2. Specify the decision rule at a 5% significance level. (Round your answer to 3 decimal places.)
Reject H0 if χ2df >
b-3. What is your conclusion?
Reject H0; quality and source of shipment are dependent
Do not reject H0; quality and source of shipment are dependent
Reject H0; quality and source of shipment are not dependent
Do not reject H0; quality and source of shipment are not dependent
c. Should the firm be concerned about the source of the shipments?
Yes
No
Question 7
Exercise 12-21
Consider the following sample data with mean and standard deviation of 17.5 and 7.4, respectively. UseTable 3.
Class Frequency
Less than 10 29
10 up to 20 95
20 up to 30 60
30 or more 17
n = 201
________________________________________
a. Using the goodness-of-fit test for normality, specify the competing hypotheses in order to determine whether or
not the data are normally distributed.
H0: The data are normally distributed with a mean of 17.5 and a standard deviation of 7.4.; HA: The data are not
normally distributed with a mean of 17.5 and a standard deviation of 7.4.
H0: The data are not normally distributed with a mean of 17.5 and a standard deviation of 7.4.; HA: The data are
normally distributed with a mean of 17.5 and a standard deviation of 7.4.
b. Calculate the value of the test statistic. (Round the z value to 2 decimal places, all other intermediate values to 4
decimal places, and final answer to 2 decimal places.)
χ2df
c. At the 5.0% significance level, what is the decision rule? (Round your answer to 3 decimal places.)
Reject H0 if χ2df >
d. What is the conclusion?
Do not reject H0; the data are normally distributed
Reject H0; the data are normally distributed
Do not reject H0; the data are not normally distributed
Reject H0; the data are not normally distributed
Exercise 12-11
Suppose you are conducting a test of independence. Specify the critical value under the following scenarios (Use
Table 3):
a. rows = 5, columns = 2, and α = 0.01. (Round your answer to 3 decimal places.)
Critical value
b. rows = 2, columns = 2, and α = 0.01. (Round your answer to 3 decimal places.)
Critical value
Question 9
Exercise 12-1
Consider a multinomial experiment with n = 276 and k = 4. The null hypothesis to be tested is H0: p1 = p2= p3 =
p4 = 0.25. The observed frequencies resulting from the experiment are (Use Table 3):
Category 1 2 3 4
Frequency 76 46 78 76
________________________________________
a. Choose the appropriate alternative hypothesis.
Not all population proportions are equal to 0.25.
All population proportions differ from 0.25.
b. Calculate the value of the test statistic.(Round intermediate calculations to 4 decimal places and your final answer
to 2 decimal places.)
χ2df
c. Calculate the critical value at a 5% significance level. (Round your answer to 3 decimal places.)
χ2α,df
d. What is the conclusion to the hypothesis test?
Reject H0 since the value of the test statistic does not exceed the critical value
Do not reject H0 since the value of the test statistic does not exceed the critical value
Reject H0 since the value of the test statistic exceeds the critical value
Do not reject H0 since the value of the test statistic exceeds the critical value
Exercise 13-35
The effects of detergent brand name (factor A) and the temperature of the water (factor B) on the brightness of
washed fabrics are being studied. Four brand names and two temperature levels are used, and six replicates for each
combination are examined. The following ANOVA table is produced.
ANOVA
Source of Variation SS df MS F p-value F crit
Sample 87 1 87.00 85.80 1.68E-11 4.085
Columns 134.44 3 44.81 44.19 9.08E-13 2.839
Interaction 7.62 3 2.54 2.50 .0728 2.839
Within 40.56 40 1.01
________________________________________ ________________________________________
Total 269.62 47
________________________________________________________________________________
________________________________________________________________________________
________________________________________
a. Can you conclude that there is interaction between detergent brand name and the temperature of the water at the
5% significance level?
No
Yes
b-1. Are you able to conduct tests based on the main effects?
Yes
No
b-2. If yes, conduct these tests at the 5% significance level. (You may select more than one answer. Single click the
box with the question mark to produce a check mark for a correct answer and double click the box with the question
mark to empty the box for a wrong answer.)
Differences exist in the average brightness of fabrics depending on the temperature of the water.
Differences do not exist in the average brightness of fabrics depending on the detergent brand name.
Differences exist in the average brightness of fabrics depending on the detergent brand name.
Differences do not exist in the average brightness of fabrics depending on the temperature of the water.

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Answer 1:

a. Part b, at least one of the proportions differs

b. 1. The test statistic is found as:

Total frequency = 340

P1=0.60, p2= 0.25, p3 = 0.15

Expected frequency, for category 1 = 0.60 *340 = 204, fr category 2 = 0.25 * 340 = 85 and for category 3 = 340 – 204 – 85 = 51.

Actual frequency = 230, 80, 30.

Test statistic = (204 – 230)2/204 + (85 – 80)2/85 + (51 – 30)2/51 = 12.25

2. (b) p < 0.005...