1) Define a problem where you test a hypothesis mean µX = (a value you choose) with the alternate hypothesis µX ≠ (the same value you have chosen) at the level of significance (α) of 0.05, for a sample size N=11, by also defining your own values for the standard deviation ( ) and mean ( ) of the sample. Show whether the hypothesis is accepted or rejected.
(Hint: Define and solve a two-sided hypothesis testing question using t(student) distribution. Check MAT271E_PART 10.pdf.)
2) Define the same problem where you test a hypothesis mean µX = (a value you choose) this time with the alternate hypothesis µX < (the same value you have chosen), for the same level of significance (α) of 0.05, same sample size N=11 and the same standard deviation ( ) and mean ( ) of the sample. Show whether the hypothesis is accepted or rejected.
(Hint: Define and solve a one-sided hypothesis testing question using t (student) distribution.)
3) Define a problem where you test a hypothesis standard deviation σX= (a value you choose) with the alternate hypothesis σX ≠ (the same value you have chosen) at the level of significance (α) of 0.10, for a sample size N=15, by also defining your own values for the standard deviation ( ) of the sample. Show whether the hypothesis is accepted or rejected.
(Hint: Define and solve a two-sided hypothesis testing question using c2 (chi-square) distribution.)
4) Define the same problem where you test a hypothesis standard deviation σX=(a value you choose) this time with the alternate hypothesis σX > (the same value you have chosen), for the same level of significance (α) of 0.10, same sample size N=15and the same standard deviation ( ) of the sample. Show whether the hypothesis is accepted or rejected.
(Hint: Define and solve a one-sided hypothesis testing question using c2 (chi-square) distribution.)
