Find the smallest test statistic out of the 40 tests and circle it. Is the corre
ID: 3217450 • Letter: F
Question
Find the smallest test statistic out of the 40 tests and circle it. Is the corresponding p-value the smallest out of all the p-values?
We begin this by generating some random data. Go to Tools (Data)Data-AnalysisRandom Number Generation. For “Number of Variables”, enter 1. For “Number of Random Numbers”, enter 40. For “Distribution”, select “Normal”. For “Parameters” enter 30 for mean and 1 for standard deviation. For “Random Seed” enter a random integer between 1 and 32767 (try to choose the number in your mind at random. Don’t pick the same number as a classmate and don’t pick the same number every time you generate random data).
We have told Excel we would like a random sample of one random variable, 40 observations, and the observations should be normally distributed with =30 and =1. Under “output options”, select “output range” and enter A1. You are telling Excel to put the observations in column A starting with cell A1. After you click OK you should see 40 numbers in cells A1 through A1000, almost all of which will be between 27 and 33.
Repeat the above instructions, except put another 40 observations from the Normal distribution with a mean of 30 and standard deviation of 1 into columns B, C , and D. Remember to have a different number for “Random Seed” each time. Otherwise, all 4 columns of numbers will be exactly the same! You should finish with a total of 160 observations in cells A1 through D40.
Pretend that each observation is the weight in grams of a machine part being produced on an assembly line. There are 40 random samples of size n=4, one in each row of the spreadsheet. There are 40 engineers working independently of each other, and all of them have taken a sample of size n-4 from the population (each engineer knows that X if normally distributed and =1, but DOES NOT know ).
All the engineers want to do a hypothesis test for with their sample. They are interested in whether or not =30 grams and suspect may actually be less than 30 grams. In other words and .
Go to cell F1 and enter =(AVERAGE(A1:D1)-30)/(1/SQRT(4)). This is the test statistic Z for the first hypothesis test.
By copying and pasting cell F1, find all 40 test statistics and place them in cells F1 through F40. Each engineer wants a significance level of = .05, so go to cell G1 and enter =(F1<-1.645)*1. We are asking Excel if the test statistic is less than -1.645. In other words, we are asking Excel if the scientist rejected and = .05. The result is either a 0 (no, wasn’t rejected) or a 1 (yes, was rejected). By copying and pasting cell G1 (see Homework 0), find a decision for all 40 hypothesis tests and place them in cells G1 through G40.
Go to cell G42 and enter =SUM(G1:G40). You are counting how many of the hypothesis tests led to a rejection.
Go to cell H1 and enter =NORMSDIST(F1). The NORMSDIST function gives you the area to the left of a value on the Z curve. In other words, you are asking for the p-value of this left-tailed hypothesis test. By copying and pasting cell H1, find the p-value for all 40 hypothesis tests and place them in cells H1 through H40.
A B C D E F G H
Explanation / Answer
Note: I am not sure what exact clarification you are looking for, but to answer the question at the beginning.
The 40 test statistics are given in the F column and the least is in the F1 cell -> -4.03417. The P value is the smallest for this statistic.
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