Question

chin researched the amount of money 150 students earned per month from jobs held during the summer. he created a table of six sample means from his collected data.

sample number	sample mean ($)
2	235
3	245
4	207
5	205
6	210

using his results, what is a valid prediction about the mean of the population?
the predicted mean of the population will be less than 200.
the predicted mean of the population will be less than 245.
the predicted mean of the population will be more than 275.
the predicted mean of the population will be more than 250.

Explanation:

Step1: Calculate the mean of the sample means

The sample means are 208, 235, 245, 207, 205, 210. The formula for the mean of a set of numbers $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here $n = 6$, and $\sum_{i=1}^{6}x_i=208 + 235+245+207+205+210=1310$. So the mean of the sample - means is $\frac{1310}{6}\approx218.33$.

Step2: Analyze the options

• Option 1: Since $218.33>200$, this option is incorrect.
• Option 2: Since $218.33 < 245$, this option is correct.
• Option 3: Since $218.33<275$, this option is incorrect.
• Option 4: Since $218.33<250$, this option is incorrect.

Answer:

The predicted mean of the population will be less than 245.