Concept explainers
To check: Whether there is sufficient evidence to conclude that phenotypes is occurring in ratio of 9:3:3:1.
Answer to Problem 18E
Yes, there is sufficient evidence to conclude that phenotypes are occurring in ratio of 9:3:3:1.
Explanation of Solution
Given:
Table is:
Phenotype | Frequency |
Tall cut | 926 |
Tall potato | 288 |
Dwarf cut | 293 |
Dwarf potato | 104 |
Ratio is 9:3:3:1.
Formula used:
The formula to compute the test statistic is
Calculation:
The proportions are:
The null and alternative hypotheses are:
The calculation for test statistic is done as:
Observed value | ||||
926 | 906.1875 | 19.8125 | 392.5352 | 0.4332 |
288 | 302.0625 | 14.0625 | 197.7539 | 0.6547 |
293 | 302.0625 | -9.0625 | 82.1289 | 0.2719 |
104 | 100.6875 | 3.3125 | 10.9727 | 0.109 |
The test statistic is:
The degree of freedom is calculated as:
The p-value using chi-square table at 1 degree of freedom is 0.6895
The p -value is above significance level. The null hypothesis does not get rejected. Thus, there is sufficient evidence to conclude that phenotypes are occurring in ratio of 9:3:3:1.
Chapter 11 Solutions
The Practice of Statistics for AP - 4th Edition
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