PRACTICE OF STATISTICS F/AP EXAM
6th Edition
ISBN: 9781319113339
Author: Starnes
Publisher: MAC HIGHER
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Question
Chapter 11.2, Problem 38E
a)
To determine
To summarize data in a two-way table.
a)
Expert Solution
Explanation of Solution
Given:
| Group | Treatment | Number of patients | Having stroke |
| 1 | Placebo | 1649 | 250 |
| 2 | Aspirin | 1649 | 206 |
| 3 | Dipyridamole | 1654 | 211 |
| 4 | Both | 1650 | 157 |
Calculation:
For constructing a two-table, we need successes and failures with each treatment. Therefore, we already know about the treatment and number of patients had a stroke. So, number of patients had a no stroke will be calculated by subtracting number of patients had a stroke from number of patients. Following table shows the two-way table:
| Treatment | Having stroke | Having no stroke | Total |
| Placebo | 250 | 1399 | 1649 |
| Aspirin | 206 | 1443 | 1649 |
| Dipyridamole | 211 | 1443 | 1654 |
| Both | 157 | 1493 | 1650 |
| Total | 824 | 5778 | 6602 |
b)
To determine
To perform chi square test of independence.
b)
Expert Solution
Answer to Problem 38E
There is convincing evidence that the difference in the effectiveness of the four treatments at the 0.05 level of significance.
Explanation of Solution
Given:
| Treatment | Having stroke | Having no stroke | Total |
| Placebo | 250 | 1399 | 1649 |
| Aspirin | 206 | 1443 | 1649 |
| Dipyridamole | 211 | 1443 | 1654 |
| Both | 157 | 1493 | 1650 |
| Total | 824 | 5778 | 6602 |
Calculation:
Null and alternative hypotheses:
Using excel formula,
| Having strock | Having no stroke | Total | ||
| Placebo | Observed | 250 | 1399 | 1649 |
| Expected | 205.81 | 1443.19 | 1649.00 | |
| (O - E)² / E | 9.49 | 1.35 | 10.84 | |
| Aspirin | Observed | 206 | 1443 | 1649 |
| Expected | 205.81 | 1443.19 | 1649.00 | |
| (O - E)² / E | 0.00 | 0.00 | 0.00 | |
| Dipyridamole | Observed | 211 | 1443 | 1654 |
| Expected | 206.44 | 1447.56 | 1654.00 | |
| (O - E)² / E | 0.10 | 0.01 | 0.12 | |
| Both | Observed | 157 | 1493 | 1650 |
| Expected | 205.94 | 1444.06 | 1650.00 | |
| (O - E)² / E | 11.63 | 1.66 | 13.29 | |
| Total | Observed | 824 | 5778 | 6602 |
| Expected | 824.00 | 5778.00 | 6602.00 | |
| (O - E)² / E | 21.22 | 3.03 | 24.24 | |
| 24.24 | chi-square | |||
| 3 | df | |||
| 2.22E-05 | p-value |
Decision: P-value = 2.22E-05< 0.05, reject H0.
Conclusion: There is convincing evidence that the difference in the effectiveness of the four treatments at the 0.05 level of significance.
Chapter 11 Solutions
PRACTICE OF STATISTICS F/AP EXAM
Ch. 11.1 - Prob. 1ECh. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Prob. 54ECh. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - Prob. 57ECh. 11.2 - Prob. 58ECh. 11.2 - Prob. 59ECh. 11.2 - Prob. 60ECh. 11.2 - Prob. 61ECh. 11.2 - Prob. 62ECh. 11.2 - Prob. 63ECh. 11.2 - Prob. 64ECh. 11 - Prob. R11.1RECh. 11 - Prob. R11.2RECh. 11 - Prob. R11.3RECh. 11 - Prob. R11.4RECh. 11 - Prob. R11.5RECh. 11 - Prob. T11.1SPTCh. 11 - Prob. T11.2SPTCh. 11 - Prob. T11.3SPTCh. 11 - Prob. T11.4SPTCh. 11 - Prob. T11.5SPTCh. 11 - Prob. T11.6SPTCh. 11 - Prob. T11.7SPTCh. 11 - Prob. T11.8SPTCh. 11 - Prob. T11.9SPTCh. 11 - Prob. T11.10SPTCh. 11 - Prob. T11.11SPTCh. 11 - Prob. T11.12SPTCh. 11 - Prob. T11.13SPT
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