Question

For a normal population, the sample mean M = 35 has the same absolute value of the z-score as the sample mean M = 43. The two samples have the same sample size n. What is the population mean?

a. 4
b. 35
c. 39
d. 43

Answer 1

C. 39

Explanation:

We are given sample means of M=35 and M=43 that have equal z-scores in absolute value but with opposite signs. This tells us the population mean lies precisely between these two values, since the z-score reflects the number of standard errors a sample mean deviates from the population mean.

Specifically, the z-score formula is:

z = (Sample mean - Population mean) / Standard error

If M=35 has a positive z-score and M=43 an equal negative z-score, the population mean must be equidistant from both.

To calculate this:

Take the average of the sample means:

(M=35 + M=43) / 2 = 39

Therefore, the population mean is 39.

The equivalent absolute z-scores but with opposite signs for the two sample means allows us to mathematically deduce the population mean falls halfway between them, which is 39 in this case.

Hope this helps! :)