Q.3.2 - The Practice of Statistics for AP

Question

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all $222$ recorded eruptions during a particular month. For this population, the median is $75$ minutes. We used Fathom software to take $500$ SRSs of size $10$ from the population. The $500$ values of the sample median are displayed in the histogram above right. The mean of the $500$ sample median values is $73.5$.

Suppose we had taken samples of size $20$ instead of size $10$. Would the spread of the sampling distribution be larger, smaller, or about the same? Justify your answer

Step-by-Step Solution

Answer

The spread of the distribution would be larger. 

Step 1 Given Information

Median is $75 .$

The sample size is $20$

Mean is $73.5$

Step 2 Explanation

We have a more precise estimate is provide by the larger sample because it contains more information in comparison to the smaller sample. Thus, it could be said that spread of the distribution would be larger.