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A census was conducted in the city of Springville. The results showed that of the

10,500
inhabitants,
3675
were children and
6825
were adults.

(a)Construct a percent bar graph for the inhabitants of Springville.

50%50%
ChildrenAdults

Let's simulate three random samples of
500
inhabitants from Springville. Press all three "Run" buttons to do so. (You can press "Run" multiple times to generate more samples to see how they vary.)
Run
Run

Sample size:
0
Number
%
of totalChildren
Adults
Run
Run

Sample size:
0
Number
%
of totalChildren
Adults
Run
Run

Sample size:
0
Number
%
of totalChildren
Adults
(b)In part (a), we calculated two different types of percentages: population percentages in the percent bar graph and sample percentages in the simulations.
The adult population percentage is the percentage of the
10,500
Springville inhabitants who are adults.
The adult sample percentage is the percentage of inhabitants who are adults in a random sample of
500
inhabitants.
True or false?
StatementTrueFalseIn any random sample of
500
Springville inhabitants, the adult sample percentage is always
50%
.
In a random sample of
500
Springville inhabitants, the adult sample percentage can be equal to the adult population percentage.
With a very large sample size, there must be no difference between the adult sample percentage and the adult population percentage.

1 answer

Let's break down your questions step-by-step.

(a) Percent Bar Graph

Inhabitants of Springville:

  • Total Inhabitants = 10,500
  • Children = 3,675
  • Adults = 6,825

To create a percent bar graph, we will calculate the percentage of children and adults in the population:

  • Percentage of Children = \( \frac{3675}{10500} \times 100 \approx 35% \)
  • Percentage of Adults = \( \frac{6825}{10500} \times 100 \approx 65% \)

You can represent these percentages in a simple bar graph as follows:

|       | 
|   65% |                Adults 
|       |
|------- |
|   35% |                Children
|       |

(b) True or False Statements

  1. In any random sample of 500 Springville inhabitants, the adult sample percentage is always 50%.

    • False. The adult sample percentage can vary depending on which individuals are included in the sample.

  2. In a random sample of 500 Springville inhabitants, the adult sample percentage can be equal to the adult population percentage.

    • True. There is a possibility that a sample could randomly contain the same proportion of adults as the overall population; however, it is not guaranteed.

  3. With a very large sample size, there must be no difference between the adult sample percentage and the adult population percentage.

    • False. While larger sample sizes tend to produce sample percentages that are closer to population percentages due to reduced variability, it is still possible to observe differences. The law of large numbers indicates that as the sample size increases, the sample mean will converge to the population mean, but "must be no difference" is too strong a statement as there can still be sampling variability.

In summary:

  1. False
  2. True
  3. False