a)
To verify the conditions for inference.
a)
Answer to Problem 31E
All conditions satisfied.
Explanation of Solution
Given:
Survey type | |||||
Red | Blue | Control | Total | ||
Color of candy | Red | 13 | 5 | 8 | 26 |
Blue | 7 | 15 | 12 | 34 | |
Total | 20 | 20 | 20 | 60 |
Calculation:
The conditions of chi square test are: Random, Independence and Large counts.
The volunteers randomly assigned to a survey, so condition of random sample is satisfied.
The sample size is 60 which is less than 10% of all population so, the condition of independent is satisfied.
The expected count of each survey is at least 5 so, condition of large count is satisfied.
b)
To find p-value using table
b)
Answer to Problem 31E
P-value 0.025 < p < 0.05
Explanation of Solution
Given:
Survey type | |||||
Red | Blue | Control | Total | ||
Color of candy | Red | 13 | 5 | 8 | 26 |
Blue | 7 | 15 | 12 | 34 | |
Total | 20 | 20 | 20 | 60 |
The value of chi square test statistic is 6.6516
Formula:
The degrees of freedom =
Calculation:
The degrees of freedom =
Using table, p-value is
0.025 < p < 0.05
c)
To find p-value using calculator
c)
Answer to Problem 31E
P-value is 0.035933
Explanation of Solution
Given:
Survey type | |||||
Red | Blue | Control | Total | ||
Color of candy | Red | 13 | 5 | 8 | 26 |
Blue | 7 | 15 | 12 | 34 | |
Total | 20 | 20 | 20 | 60 |
The value of chi square test statistic is 6.6516
Formula:
The degrees of freedom =
Calculation:
The degrees of freedom =
Using excel formula, =CHIDIST(6.6516,2)
P-value = 0.035944 = 3.5944%
Therefore, there is 3.5944% chance of obtaining the sample results of more extreme, when the distribution of candy type is truly the same for each survey type.
d)
To explain conclusion.
d)
Answer to Problem 31E
There is no convincing evidence that the distribution of candy type is not the same for each survey type.
Explanation of Solution
Given:
Survey type | |||||
Red | Blue | Control | Total | ||
Color of candy | Red | 13 | 5 | 8 | 26 |
Blue | 7 | 15 | 12 | 34 | |
Total | 20 | 20 | 20 | 60 |
The value of chi square test statistic is 6.6516
P-value = 0.035944
Calculation:
Decision: P-value > 0.01, fail to reject H0.
Conclusion: There is no convincing evidence that the distribution of candy type is not the same for each survey type.
Chapter 11 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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