Concept explainers
To check: Whether the population of Froot Loops that have been produced contain an equal proportion of each flavor.
Answer to Problem 16E
No, the population of Froot Loops that have been produced do not contain an equal proportion of each flavor.
Explanation of Solution
Given:
Flavour | Count |
Orange | 28 |
Lemon | 21 |
Cherry | 16 |
Raspberry | 25 |
Blueberry | 14 |
Lime | 16 |
Formula used:
The formula to compute the test statistic is
Calculation:
The null and alternative hypotheses are:
The calculation for test statistic is done as:
Observed value | ||||
28 | 20 | 8 | 64 | 3.2 |
21 | 20 | 1 | 1 | 0.05 |
16 | 20 | -4 | 16 | 0.8 |
25 | 20 | 5 | 25 | 1.25 |
14 | 20 | -6 | 36 | 1.8 |
16 | 20 | -4 | 16 | 0.8 |
The test statistic is:
The degree of freedom is calculated as:
The p-value using chi-square table at 5 degree of freedom is 0.162.
The p -value is above significance level. The null hypothesis does not get rejected. Thus, there is insufficient evidence to conclude that the population of Froot Loops that have been produced do not contain an equal proportion of each flavor.
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