(a)
Find the expected balls to be drawn.
(a)
Answer to Problem 9EA
The expected ball to be drawn is 12.
Explanation of Solution
Calculation:
A set of 10 Ping-Pong balls are considered and there are 120 draws from the bowl.
The expected ball to be drawn is,
Hence, the expected ball to be drawn is 12.
(b)
Explain how the decisions follow from the data.
(b)
Explanation of Solution
Calculation:
Chi-square test statistic:
The test statistic for chi-square distribution is,
With
For Ball set A:
The
Ball no. |
Observed Frequency | Expected frequency |
0 | 13 | |
1 | 11 | |
2 | 16 | |
3 | 11 | |
4 | 5 | |
5 | 12 | |
6 | 12 | |
7 | 19 | |
8 | 5 | |
9 | 16 | |
Total | 120 |
The test statistic is,
Hence, the value of
For Ball set B:
The expected values are,
Ball no. |
Observed Frequency | Expected frequency |
0 | 22 | |
1 | 8 | |
2 | 7 | |
3 | 8 | |
4 | 19 | |
5 | 20 | |
6 | 10 | |
7 | 11 | |
8 | 6 | |
9 | 9 | |
Total | 120 |
The test statistic is,
Hence, the value of
For Ball set C:
The expected values are,
Ball no. |
Observed Frequency | Expected frequency |
0 | 12 | |
1 | 10 | |
2 | 14 | |
3 | 10 | |
4 | 11 | |
5 | 10 | |
6 | 20 | |
7 | 12 | |
8 | 12 | |
9 | 9 | |
Total | 120 |
The test statistic is,
Hence, the value of
For Ball set D:
The expected values are,
Ball no. |
Observed Frequency | Expected frequency |
0 | 16 | |
1 | 7 | |
2 | 12 | |
3 | 14 | |
4 | 15 | |
5 | 5 | |
6 | 10 | |
7 | 21 | |
8 | 11 | |
9 | 9 | |
Total | 120 |
The test statistic is,
Hence, the value of
There are 10 value. The degrees of freedom is,
Hence, the degrees of freedom is 9.
From A CHI-SQUARE TABLE, the value corresponding to the 9 degrees of freedom for 10% level is 14.68, 5% level is 16.92, and the 1% level is 21.67.
It is clear that the ball set A and set D are in between the level 1% to 10% indicates that the sets are marginal and it would be retested.
The ball set B test value is greater than the critical values this indicates that the set B is rejected outright, and ball set C test value is less than the critical value which implies that the set C is accepted.
(c)
Test the Ball set A and D by using retest values.
Comment on the results.
(c)
Explanation of Solution
Calculation:
For Ball set C:
The expected values are,
Ball no. |
Observed Frequency | Expected frequency |
0 | 19 | |
1 | 9 | |
2 | 10 | |
3 | 12 | |
4 | 7 | |
5 | 15 | |
6 | 19 | |
7 | 10 | |
8 | 12 | |
9 | 7 | |
Total | 120 |
The test statistic is,
Hence, the value of
For Ball set D:
The expected values are,
Ball no. |
Observed Frequency | Expected frequency |
0 | 8 | |
1 | 15 | |
2 | 22 | |
3 | 11 | |
4 | 15 | |
5 | 8 | |
6 | 17 | |
7 | 9 | |
8 | 8 | |
9 | 7 | |
Total | 120 |
The test statistic is,
Hence, the value of
The ball set D test value is greater than the critical values of 5% level this indicates that the set D is rejected, and ball set A test value is less than the critical value which implies that the set A is accepted.
Want to see more full solutions like this?
Chapter 28 Solutions
Statistics
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman