(a)
To find the
(a)
Answer to Problem 27.22AYK
The color which attracted more insects is Yellow.
Explanation of Solution
In the question, it is given that the researchers want to examine the insects trapped on the boards with different colors. Thus, the data is given on the insects trapped by the different colored boards. Now, to find the median we will use the excel formula which is,
Thus, the formula used will be as:
Blue | Green | White | Yellow | |
16 | 37 | 21 | 45 | |
11 | 32 | 12 | 59 | |
20 | 20 | 14 | 48 | |
21 | 29 | 17 | 46 | |
14 | 37 | 13 | 38 | |
7 | 32 | 20 | 47 | |
Median= | =MEDIAN(AZ3:AZ8) | =MEDIAN(BA3:BA8) | =MEDIAN(BB3:BB8) | =MEDIAN(BC3:BC8) |
And the result will be as:
Blue | Green | White | Yellow | |
16 | 37 | 21 | 45 | |
11 | 32 | 12 | 59 | |
20 | 20 | 14 | 48 | |
21 | 29 | 17 | 46 | |
14 | 37 | 13 | 38 | |
7 | 32 | 20 | 47 | |
Median= | 15 | 32 | 15.5 | 46.5 |
Now, by looking at the median, the color which attracted more insects is Yellow and then after that most attracted insects by color is White, as their median is largest and second largest.
(b)
To find out what hypotheses does ANOVA test and Kruskal-Wallis test.
(b)
Explanation of Solution
In the question, it is given that the researchers want to examine the insects trapped on the boards with different colors. Thus, the data is given on the insects trapped by the different colored boards. Now, the hypotheses defined by the ANOVA test will be as:
And the hypotheses defined by the Kruskal-Wallis test will be as:
Null hypothesis: Insect trapped have same distribution in all groups.
Alternative hypothesis: They are all different from each other.
(c)
To find out what are
(c)
Answer to Problem 27.22AYK
Explanation of Solution
In the question, it is given that the researchers want to examine the insects trapped on the boards with different colors. Thus, the data is given on the insects trapped by the different colored boards. Since there are four colors therefore there are four population, thus,
Now, we will arrange the insects trapped by different colors in order and assign ranks with the help of Excel using the sort and filter command in the home tab. Thus, the result will be as:
Label | Data | Rank |
Blue | 16 | 7 |
Blue | 11 | 2 |
Blue | 20 | 10 |
Blue | 21 | 12.5 |
Blue | 14 | 5.5 |
Blue | 7 | 1 |
Green | 37 | 17.5 |
Green | 32 | 15.5 |
Green | 20 | 10 |
Green | 29 | 14 |
Green | 37 | 17.5 |
Green | 32 | 15.5 |
White | 21 | 12.5 |
White | 12 | 3 |
White | 14 | 5.5 |
White | 17 | 8 |
White | 13 | 4 |
White | 20 | 10 |
Yellow | 45 | 20 |
Yellow | 59 | 24 |
Yellow | 48 | 23 |
Yellow | 46 | 21 |
Yellow | 38 | 19 |
Yellow | 47 | 22 |
(d)
To calculate the Kruskal-Wallis statistics H and find how many degrees of freedom should you use for the chi-square approximation to its null distribution and use chi-square table to give approximate P-value and what does the test lead you to conclude.
(d)
Answer to Problem 27.22AYK
Explanation of Solution
In the question, it is given that the researchers want to examine the insects trapped on the boards with different colors. Thus, the data is given on the insects trapped by the different colored boards. Since there are four colors therefore there are four population, thus,
And the arrange order is given above in part (c). Thus, we will sum the rank for each color and the result will be as:
Colours | Sum of ranks |
Blue | 38 |
Green | 90 |
White | 43 |
Yellow | 129 |
Now, the Kruskal-Wallis statistics H can be calculated as:
The degrees of freedom will be as:
Now, we will look at the chi-square table for the P-value as:
As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,
Thus, we have sufficient evidence to conclude that the insects trapped by different colors are statistically different from each other.
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Chapter 27 Solutions
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