Let x1,x2,,x6x1,x2,,x6 represent data observed from a random sample of $n = 6 taken from a population of values described by the following probability density function.

f(xi;)=e(xi)xiis less than 2.018. In other words, reject the null hypothesis if XMin<2.018XMin<2.018. The probability density function of this statistic XMinXMin is provided:f(xMin;)=nen(xMin)xMinf(xMin;)=nen(xMin)xMin

What value of was used in the derivation of this statistical test?

The data below are the observed values of the sample:

1. 2.95,2.21,2.43,2.11,2.77,3.122.95,2.21,2.43,2.11,2.77,3.12Does this sample support the null hypothesis above? Explain your answer. (Note, the sort function will sort data points in ascending order.)

Revisiting the statistical test in (a), based on n=6n=6 and the found value of : compute the probability of concluding that =2=2 when in fact =1.8=1.8.

In an attempt to decrease the probability of committing a Type II error, the value of was increased from the value in (a) to 0.20. From a sample of n=6n=6 and a =0.20=0.20, what value(s) ofXMinXMin would result in a rejection of the null hypothesis?