Suppose that your statistics instructor gave six examinations during the semeste

Question

Suppose that your statistics instructor gave six examinations during the semester. You received the following grades (percentage correct): 66, 87, 59, 81, 55, and 54. Instead of averaging the six scores, the instructor indicated he would randomly select 4 grades and report that grade to the student records office.

How many different samples, without replacement, of 4 test grades are possible? diferent samples

Compute the mean of the sample means and compare it with the population mean. (Round the final answers to 2 decimal places.)

  Both means are

Would the result be different from dropping the lowest score?

How many different samples, without replacement, of 4 test grades are possible? diferent samples

Compute the mean of the sample means and compare it with the population mean. (Round the final answers to 2 decimal places.)

  Both means are

Would the result be different from dropping the lowest score?

Explanation / Answer

66, 87, 59, 81, 55, 54.

There are 6 values and we can sample 4 of them in 6C4 = 15 ways.

Sum of values = 402.

Population mean = 67.

When we add the values of all the samples, each value will repeat 5C3 = 10 times.

Thus mean of sample means = (10 * 402 / 4) / 15 = 67.

Both means are same.

If the lowest score is dropped, the result won't be different as the end results are not value dependent.

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