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

9000
inhabitants,
2880
were children and
6120
were adults.

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

50%50%
ChildrenAdults

Let's simulate three random samples of
500
inhabitants from Winterdale. 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
9000
Winterdale 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 a random sample of
500
Winterdale inhabitants, the adult sample percentage can be equal to the adult population percentage.
Any random sample of
500
Winterdale inhabitants will always have
250
adults.
With a very large sample size, there might be a difference between the adult sample percentage and the adult population percentage, but the difference should be small.

1 answer

Let's break down the information provided step-by-step.

Part (a): Percent Bar Graph for the Inhabitants of Winterdale

In the census, we have:

  • Total inhabitants: 9000
  • Total children: 2880
  • Total adults: 6120

To calculate the percentages:

  1. Percentage of Children: \[ \text{Percentage of Children} = \left(\frac{2880}{9000}\right) \times 100 \approx 32% \]

  2. Percentage of Adults: \[ \text{Percentage of Adults} = \left(\frac{6120}{9000}\right) \times 100 \approx 68% \]

Thus, the percent bar graph would show:

  • Children: 32%
  • Adults: 68%

Part (b): True or False Statements

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

    • True. It's possible for the sample taken to reflect exactly the overall population percentage, although it's not guaranteed.

  2. Any random sample of 500 Winterdale inhabitants will always have 250 adults.

    • False. The number of adults in a sample of 500 will vary based on random sampling. While on average, you might expect around 68% to be adults (which would be approximately 340 adults), it can vary in different random samples.

  3. With a very large sample size, there might be a difference between the adult sample percentage and the adult population percentage, but the difference should be small.

    • True. Larger sample sizes tend to yield sample percentages that are closer to the population percentages due to the Law of Large Numbers, although small differences can still occur due to sampling variability.

In summary:

  • Statement 1: True
  • Statement 2: False
  • Statement 3: True