Question

javier and ercilia are supervisors at a shopping mall. each was given the task of estimating the mean distance that shoppers live from the mall. they each randomly surveyed 100 shoppers. the samples yielded the following information.

	javier	ercilia
$s$	4.0 miles	7.0 miles

(a) how can you determine which survey was correct?
\bigcirc ercilias survey was correct because the standard deviation is greater than the mean distance shoppers live from the mall.
\bigcirc javiers survey was correct because the standard deviation is only 2.0 miles away from the mean distance shoppers live from the mall.
\bigcirc javiers survey was correct because the standard deviation is less than the mean distance shoppers live from the mall.
\bigcirc ercilias survey was correct because the standard deviation is only 1.0 mile away from the mean distance shoppers live from the mall.
\bigcirc there is no way to determine from these numbers which survey was correct.
(b) explain what the difference in the results of the surveys implies about the data.
\bigcirc the difference in the results shows that javiers sample had a larger standard deviation than ercilias sample. this shows that there is not any variability in the distances that people live from the mall.
\bigcirc the difference in the results shows that javiers sample had a larger standard deviation than ercilias sample. this shows that, although the mean distance appears to be around 6 miles, there is probably some variability in the distances that people live from the mall.
\bigcirc the difference in the results shows that javiers sample had a smaller standard deviation than ercilias sample. this shows that there is not any variability in the distances that people live from the mall.
\bigcirc the difference in the results shows that javiers sample had a smaller standard deviation than ercilias sample. this shows that, although the mean distance appears to be around 6 miles, there is probably some variability in the distances that people live from the mall.
(c) if the two histograms depict the distribution of values for each supervisor, which one depicts ercilias sample? how do you know?
two histograms are shown, (a) has a peak at 6 and other bars, (b) has equal - height bars
\bigcirc histogram (a) depicts ercilias sample because it appears to show a larger range of values.
\bigcirc histogram (b) depicts ercilias sample because it appears to show a larger range of values.

Explanation:

Part (a)

To determine which survey is correct, we analyze the options. Standard deviation measures data spread, but mean and standard deviation alone don't indicate correctness as both samples have the same mean but different spreads. The other options' reasoning about standard deviation relative to mean is flawed (e.g., standard deviation magnitude relative to mean doesn't determine correctness). So, no way to tell from these numbers.

Javier's standard deviation (\(s = 4.0\)) is smaller than Ercilia's (\(s = 7.0\)). A larger standard deviation means more variability. So Javier's sample has less spread, Ercilia's more. The correct option notes Javier's smaller SD and that mean ~6 but there's variability (since SDs differ, data has spread).

Ercilia's sample has a larger standard deviation (7.0 vs. Javier's 4.0), meaning a larger range of values (more spread out). Histogram (b) has bars of equal height, suggesting a more uniform (larger range) distribution, while (a) has a peak at 6 (smaller spread). Wait, no—wait, the options: Histogram (b) is uniform, showing a larger range? Wait, no, recheck: Ercilia has larger SD, so her data is more spread. Histogram (b) has equal - height bars, implying a wider range (more spread), while (a) has a peak (narrower). Wait, the options: "Histogram (b) depicts Ercilia's sample because it appears to show a larger range of values." Wait, no—wait, maybe I mixed up. Wait, Ercilia's SD is 7, Javier's 4. So Ercilia's data is more spread. Histogram (b) has bars of equal height, which would represent a more uniform (wider range) distribution, so it's Ercilia's. Wait, the options: the second option (Histogram (b)) says it shows a larger range. Wait, no, the first option says (a) shows larger range, second (b). Wait, no—wait, Histogram (a) has a peak at 6, so data is clustered around 6 (smaller SD, Javier). Histogram (b) has equal bars, so data is spread more (larger SD, Ercilia). So Histogram (b) depicts Ercilia's sample because it shows a larger range (more spread out).

Answer:

There is no way to determine from these numbers which survey was correct.

Part (b)