Question:

Pascal is a high level programming language used frequently in microprocessors. An experiment was conducted to investigate the proportion of Pascal variables that are array variables, which are less efficient in terms of execution time. Twenty variables are randomly selected from a set of Pascal programs and Y, the number of array variables, is recorded. Suppose we want to test the hypothesis that Pascal is more efficient language than Algol, in which 20% of the variables are array variables. That is, we will test H ₀ : p =.20 against H _a : p > .20 , where p is the probability of observing an array variable on each trial (Assume that the 20 trials are independent).

1. Find α for the rejection ( Y ≥ 8 )
2. Find α for the rejection ( Y ≥ 5 )
3. Find β for the rejection Y ≥ 8 if p = 0.5 (Note: Past experience has shown that approximately half the variables in most Pascal programs are array variables.)
4. Find β for the rejection Y ≥ 5 if p = .5
5. Which of the rejection regions Y ≥ 8 or Y ≥ 5 is more desirable if you want to minimize the probability of a Type I error? Type II error?
6. Find the rejection region of the form Y ≥ α so that α is approximately equal to .01.

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