CLT: Question 1

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Ourtown Health Department reported that the height of women in the city is approximately normally distributed with a mean of 5 feet, 4 inches (i.e., 64 inches) and a standard deviation of 3 inches.

Suppose we select a random sample of five women from our school, measure the height of each, and calculate the sample mean. If we wished to know whether the height of women at our school is typical of the height of women in Ourtown, how should we compare our sample data to information we have about the Ourtown population distribution?

We should compare the sample mean to the population distribution of Ourtown women as we do with an individual score.

Sorry, this answer is incorrect!

Comparing the sample mean to the population distribution, as we do with individual scores, would not be appropriate because possible means are not distributed in the same way as individual scores.

We should compare each individual score in our sample, one at a time, to the population of individual scores.

Sorry, this answer is incorrect!

It’s okay to compare individual scores with a population distribution of individual scores, but we can do better when we have a sample mean. We should use the sample mean to make a comparison.

There really isn’t a way to make any worthwhile comparison.

Sorry, this answer is incorrect!

Although it’s not correct to compare our sample mean with a distribution of individual scores, another type of comparison is done quite often and is certainly worthwhile.

We should compare this sample mean to a sampling distribution of all possible means for samples of 5 women from the population of women in Ourtown.

Correct! It is appropriate to compare our sample mean with a distribution that is made up of all possible sample means (a sampling distribution of means).  To compare our sample mean with a distribution of individual scores would be comparing apples to pickles. EXCELLENT!

 

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