Statistics 104 - Term Project
Due: June 4, 2018
The Excel le "term project.xlsx" contains data from several distributions. For this project
you are asked to carry out the hypothesis tests as described below using non-parametric procedures
introduced in class and comparing to results from normal and t-tests. In all analyses, carry out
some diagnostics in the form. of normal probability plots, histograms, boxplots and other methods
you think are appropriate.
1 Analysis of sample 1: for this data carry out a test of the hypothesis H0 : = 0 vs Ha : > 0,
using an appropriate non-parametric test based on the median, mean or a 10% trimmed mean.
Compare your results to the one-sample t-test.
2 For sample 2 test the following hypothesis:
a H0 : 1 = 2 vs Ha : 1 < 2
b H0 : 1 = 2 vs Ha : 1 ̸= 2
As in part (a) for the test comparing means, compare your results to the two-sample t-test. For
the comparison of variances, compare your results to an F-test for equality of variances.
3 For the data in sample 3 compare the distributions using the Kolmogorov-Smirnov test.
4 For the data from sample 4 test the hypothesis H0 : 1 = 2 = 3 = 4 vs the alternative that
not all means are equal. Compare your results to the F-test from ANOVA.
In all cases, assess the distribution your data is sampled from using plots and other diagnostic
tools. Discuss which approach you prefer and why. Also, discuss various non-parametric tests
and which one you feel is the most appropriate for each of the samples. Summarize your results
in the form. of written report in the style. of a scienti c article. You will be graded on both the
statistical methods used and the write-up. You are expected to create randomization (permutation
distributions or Monte Carlo simulations) for parts of the project. Using established tests in R such
as ks.test for Kolmogorov-Smirnov is not acceptable.