Question

consider these sample means for the number of weekend hours spent studying for a monday exam.
which statements are true? check all that apply.
the variation in the sample means is less than 5.
the variation in the sample means makes population predictions invalid.
the actual population mean most likely will be between 4 and 8.
the sample means can be used to make predictions about the population mean.
the population mean is greater than 8.
sample | sample mean
1 | 8
2 | 5
3 | 6
4 | 4

Explanation:

Step1: Find range of sample means

Range = Max - Min = $8 - 4 = 4$

Step2: Evaluate first statement

Variation (range) = 4 < 5, so this is true.

Step3: Evaluate second statement

Sample means with small variation are valid for population predictions, so this is false.

Step4: Evaluate third statement

Sample means range from 4 to 8, so population mean is likely in this interval, this is true.

Step5: Evaluate fourth statement

Sample means are used to estimate population mean, so this is true.

Step6: Evaluate fifth statement

All sample means are ≤8, so population mean is not greater than 8, this is false.

Answer:

• The variation in the sample means is less than 5.
• The actual population mean most likely will be between 4 and 8.
• The sample means can be used to make predictions about the population mean.