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 9.
sample sample mean
1 8
2 5
3 6
4 4

Explanation:

Step1: Calculate range of sample means

Range = Max - Min. Max = 8, Min = 4. Range = 8 - 4 = 4. Since 4 < 5, the variation in the sample means is less than 5.

Step2: Analyze population prediction validity

Sample means can still be used for population predictions even with some variation. The variation here is not extreme enough to make predictions invalid.

Step3: Consider population - mean range

The sample means are 4, 5, 6, 8. The actual population mean is likely to be in the range of these sample - mean values, so it is most likely between 4 and 8.

Step4: Recall sample - mean purpose

Sample means are used to make predictions about the population mean.

Step5: Check population - mean upper - bound

The largest sample mean is 8, so it is not likely that the population mean is greater than 9.

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.