You will simulate a hypothesis test 200 times to demonstrate the significance level of the test. This means you will randomly select 200 samples of 36 values and use the statistics from this sample to test H₀: m = 250 against H₁: m not equal to 250 at the 0.10 significance level. You will randomly select these samples from a population with mean 250 and standard deviation 60.

1. Is H₀ true or false when you perform each of these tests? Explain.

2. What is(are) the critical value(s) for this test? Did you use the Z or T table? Explain.

3. If we test this hypothesis 200 times, how many times would you guess, we will
    reject H_o? Explain.

4. Proceed through TOOLS--DATA ANALYSIS--RANDOM NUMBER GENERATION.
    When the window appears fill the fields with the following information:
    Number of Variables: 36 (this will fill 36 columns with random values)
    Number of Random Numbers: 200 (this will fill each column with 200 random
    values)
    Distribution: Normal
    Mean: 250
    Standard Deviation: 60
    Random Seed: Enter a number of your choice
    Output Options: Click the circle beside NEW WORKSHEET PLY (puts output on
    a new sheet)

5. The new worksheet will appear with the random values. If we let each row be a
    random sample, then we have 200 random samples of 36 values. Move to cell AL1
    to enter =average(A1:AJ1) to obtain the mean of the first sample. In cell AM1
    enter =stdev(A1:AJ1) to obtain S for the first sample. Then in cell AN1 enter
    =AM1/sqrt(count(A1:AJ1)). What did we just compute? Finally in cell AO1 (letter
    O) enter =standardize(AL1,250,AN1). The last statement computes the T or Z
    statistic when the value to be standardized to a T or Z statistic is in cell AL1, the
    mean is 250, and the standard deviation is in cell AM1. Try this on paper or with
    your calculator to convince yourself.

6. Select cells AL1 through AO1, then copy and paste the information in these cells
    AL through AO from row 2 through 200. The result is 200 T statistics in column AO.
    Now to count the values that fall in the rejection region, enter the following formula
    in cell AP1, =countif(AO1:AO200,"<-1.645") + countif(AO1:AO200,">1.645")
    where + 1.645 are the critical values for the test.

7. Compute the percent of the tests that result in rejection in cell AR1 by entering
    =AP1/200*100. How does this percentage compare with the significance level?

8. Relate your findings to the definition of the significance level and Type I error?
 
 
 

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