Reported Height | 68 | 71 | 63 | 70 | 71 | 60 | 65 | 64 | 54 | 63 | 66 | 72 |
Measured Height | 67.9 | 69.9 | 64.9 | 68.3 | 70.3 | 60.6 | 64.5 |
67.0 |
55.6 | 74.2 | 65 | 70.8 |
Difference(d) | 0.1 | 1.1 | -1.9 | 1.7 | 0.7 | -0.6 | 0.5 | -3 | -1.6 | -11.2 | 1 | 1.2 |
Rank(d) | 1 | 6 | 10 | 9 | 4 | 3 | 2 | 11 | 8 | 12 | 5 | 7 |
Signed Rank | +1 | +6 | -10 | +9 | +4 | -3 | +2 | -11 | -8 | -12 | +5 | +7 |
a)
Null and Alternative Hypotheses:
There is no difference in median between self reported heights and measured heights .
There is a difference in median between self reported heights and measured heights .
b)
Here n=12
The sum of positive ranks is:
\
and the sum of negative ranks is:
c)
The test statistic is
d)
The critical value for the significance level provided, and the type of tail specified is , and the null hypothesis is rejected if .
e)
Since in this case , there is not enough evidence to claim that the population median of differences is different than 0, at the significance level.
Thus we can conclude that there is a significant difference in median between self reported heights and measured heights.
3) Wilcoxon Rank-Sum Test
Male | Rank | Female | Rank |
522 | 21 | 264 | 15 |
127 | 9 | 181 | 12 |
740 | 25 | 267 | 17 |
49 | 2 | 384 | 19 |
230 | 13 | 98 | 6 |
316 | 18 | 62 | 3 |
590 | 24 | 126 | 8 |
466 | 20 | 89 | 5 |
121 | 7 | 531 | 22 |
578 | 23 | 130 | 10 |
78 | 4 | 175 | 11 |
265 | 16 | 44 | 1 |
250 | 14 | ||
13 196 |
12 129 |
The sum of ranks for sample 1(Male) is:
and the sum of ranks of sample 2(Female) is:
Hence, the test statistic is .
The following null and alternative hypotheses need to be tested:
The two populations of men and woman have same median cholesterol levels .or : Median (Difference) = 0
The two populations of men and woman have different median cholesterol levels .or : Median (Difference) 0
Observe that both sample sizes are greater than 10, then we can use normal approximation. The following z-statistic will be used.
The z-statistic is computed as follows:
Based on the information provided, the significance level is , and the critical value for a two-tailed test is .The rejection region for this two-tailed test is .
Since it is observed that , it is then concluded that the null hypothesis is not rejected.
Using the P-value approach: The p-value is , and since , it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population median of differences is different than 0, at the 0.05 significance level.
Graphically:
Wilcoxon signed-ranks test for method Services data of self-reported and measured his for d evidence to...
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