Demonstrate Non-Parametric Statistics. Math Problem

Math Problems
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Solution 1
The probability that a randomly selected observation exceeds the mean of a normal distribution is equal to 0.5. This is because the normal distribution is symmetric about the mean.
Solution 2
The probability that a randomly selected observation exceeds the median of a normal distribution is also 0.5. This is because the normal distribution is symmetric about its mean, median and mode.
Solution 3
The probability that a randomly selected observation exceeds the mean of a non-normal distribution is not 0.5. This is because it is not mandatory for the non-normal distribution to be symmetrical about its mean.
Solution 4
The probability that a randomly selected observation exceeds the median of a non-normal distribution is equal to 0.5. This is because the median is the 50th percentile of the distribution.
Solution 5
There are four assumptions or circumstances, which are as follows.
1 The observations depend on one another.
2 The dependent variable needs to be continuous (interval/ratio).
3 The dependant variable is normally distributed.
4 The dependent variable contains an outlier.
Solution 6
The name of an alternative nonparametric test is Wilcoxon signed rank test. The hypothesis that the estimate depends on chance is known as the null hypothesis. Its complement is known as the alternative hypothesis.
Solution 7
cost

20427

27255

22115

23256

21887

24255

19852

23624

25885

28999

20836

Solution 8
Here, we will have to compare the probability distribution of the percentage of two sectors. For this purpose, we have chosen the non-parametric Wilcoxon Rank Sums test.
The test statistic is 66, which is greater than the lower TL value of 63. Thus, it is not possible for us to reject the null hypothesis.
Solution 9
The p-value of the test greater than 0.05; we have not rejected the null hypothesis with a = 0.05, as we know that the p-value needs to be more than 0.05.
Solution 10
We will use the Wilcoxon Signed Rank Test: Difference=After-Before
The absolute value of difference is arranged in an increasing order.
0, 3 (+), 4(-), 6(+), 6(+), 7(+), 9(+), 14(+),15(+),17(+)
The next step is to rank these absolute values.
1, 2, 3.5,3.5, 5, 6, 7, 8, 9
Here we have ignored 0 because it occurs with zero probability.
The Wilcoxon test st...