Question

harold took five different samples of thirty - five randomly selected students from the 520 students he surveyed. the means of the samples are shown below.

sample	mean
sample 2	3.2
sample 3	4.1
sample 4	4.6
sample 5	3.1

the predicted mean of the population will fall between

3.1 and ______.

o 1.5
o 3.4
o 3.7

Explanation:

Step1: Find the minimum and maximum of sample means

The sample means are 3.4, 3.2, 4.1, 4.6, 3.1. The minimum is 3.1 and the maximum is 4.6.

Step2: Determine the range for population mean prediction

When using sample - means to predict the population mean, a common approach (assuming no other information about standard - error etc.) is to consider the range of the sample means. Since the lower bound given is 3.1, the upper bound is the maximum of the sample means which is 4.6. But among the given options, we need to find the closest reasonable value. We calculate the mean of the sample means: $\bar{x}=\frac{3.4 + 3.2+4.1+4.6+3.1}{5}=\frac{18.4}{5}=3.68\approx3.7$.

Answer:

3.7