Statistics and probablity assignment due 11:59 est today open office only please

HW 13

1. On sheet 1, our operational hypothesis H0 is that we have a normal process with mean and standard deviation given in cells D1 and D2 respectively. We wish to test whether or not data (given in cells A1:A100) comes from this process. We will have three different tests.
   
   Test 1: Is the average of the data (D3) in a 90% symmetric about the mean confidence interval for the average? Construct this interval, giving its lower and upper bounds in F5 and F6. Determine in F7 whether or not the average is in this interval.
   
   Test 2: Is the average of the data (D3) in a 90% one-sided to the left confidence interval for the average? Construct this interval, giving its upper bound in F9. Determine in F10 whether or not the average is in this interval.
   
   Test 3: Is the average of the data (D3) in a 90% one-sided to the right confidence interval for the average? Construct this interval, giving its upper bound in F12. Determine in F13 whether or not the average is in this interval.
   
   

2. A normal random variable has unknown mean and known standard deviation given in D2. It is sampled five hundred times with the results in column A. Determine the average of the data in D1. If this average is to be in a (D4)% confidence interval for an average over a sample of size five hundred, give lower and upper bounds on the mean of the underlying normal random variable in D5 and D6.
   
   

3. A normal random variable has unknown mean and known standard deviation in E1. We wish to sample this enough times to be (E2)% confident that the mean of our sample is within E3 of the true mean. How large of a sample size is needed? Give the minimal such sample size in B1. Accuracy in B1 is allowed to within 5% - remember that sampling is expensive!