An analysis of variance of the yields of five different varieties of wheat, observed on one plot each at each of six different locations. The data from this randomized block design are listed here: \(\begin{array}{|c|c|} \hline Varieties & Location 1& Location 2& Location 3& Location 4& Location 5& Location 6 \\ \hline A& 35.3& 31.0& 32.7& 36.8& 37.2& 33.1 \\ \hline B& 30.7& 32.2& 31.4& 31.7& 35.0& 32.7\\ \hline C& 38.2& 33.4& 33.6& 37.1& 37.3& 38.2\\ \hline D& 34.9& 36.1& 35.2& 38.3& 40.2& 36.0\\ \hline E& 32.4& 28.9& 29.2& 30.7& 33.9& 32.1\\ \hline \end{array}\) a. Use the appropriate nonparametric test to determine whether the data provide sufficient evidence to indicate a difference in the yields for the five different varieties of wheat. Test using \(\alpha\alpha=.05\). b. How do the analysis of variance F test compare with the test in part a? Explain.

Assuming the null hypothesis is true, what is the probability that our z-test statistic would fall outside the z-critical boundaries (in the tails of the distribution the region of rejection) for anв \(\alpha=0.05?\)

\(\frac{8!}{(5!\times3!)}\)

The area between \(z=0\) and \(z= 1.1\) under the standard nomad curve is ?

Find the probability density function of \(Y=e^{X}\), when X is normally distributed with parameters \(\mu\ \text{and}\ \sigma^{2}\). The random variable Y is said to have a lognormal distribution (since log Y has a normal distribution) with parameters \(\mu\ \text{and}\ \sigma^{2}\)

A population of values has a normal distribution with \(\displaystyle\mu={198.8}\) and \(\displaystyle\sigma={69.2}\). You intend to draw a random sample of size \(\displaystyle{n}={147}\). Find the probability that a sample of size \(\displaystyle{n}={147}\) is randomly selected with a mean between 184 and 205.1. \(\displaystyle{P}{\left({184}{<}{M}{<}{205.1}\right)}=\)? Write your answers as numbers accurate to 4 decimal places.