Questions: Why will random samples from a given population not have the same mean? Sample means will vary because the data values selected for samples are not randomly chosen. Sample means will vary because for each sample the same data values are selected. Sample means will vary because the data values are randomly selected from different populations.

Why will random samples from a given population not have the same mean? Sample means will vary because the data values selected for samples are not randomly chosen. Sample means will vary because for each sample the same data values are selected. Sample means will vary because the data values are randomly selected from different populations.

Transcript text: Why will random samples from a given population not have the same mean? Sample means will vary because the data values selected for samples are not randomly chosen. Sample means will vary because for each sample the same data values are selected. Sample means will vary because the data values are randomly selected from different populations.

Solution

Solution Steps

Step 1: Understanding Random Sampling

Random samples from a given population will not have the same mean because each sample is a subset of the population, and the data values are randomly selected. This randomness leads to variability in the sample means.

Step 2: Variability in Sample Means

The variability in sample means arises because different samples may contain different data values from the population. This is due to the random selection process, which ensures that each sample is likely to be different.

Step 3: Clarifying Misconceptions

The statement that sample means will vary because the data values are not randomly chosen is incorrect. In fact, sample means vary precisely because the data values are randomly selected from the population, not because they are not randomly chosen.