A factory packages mixed nuts made with only almonds and cashews. In one container of

Question

7500
mixed nuts,
5475
of them are almonds and
2025
of them are cashews.

(a)Construct a percent bar graph for the mixed nuts in the container.

50%50%
AlmondsCashews

Let's simulate three random samples of
125
mixed nuts from the container. 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 totalAlmonds
Cashews
Run
Run

Sample size:
0
Number
%
of totalAlmonds
Cashews
Run
Run

Sample size:
0
Number
%
of totalAlmonds
Cashews
(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 almond population percentage is the percentage of the
7500
mixed nuts that are almonds.
The almond sample percentage is the percentage of mixed nuts that are almonds in a random sample of
125
mixed nuts.
True or false?
StatementTrueFalseIn any random sample of
125
mixed nuts, the almond sample percentage must always be equal to the almond population percentage.
In any random sample of
125
mixed nuts, the almond sample percentage is always
50%
.
With a very large sample size, there must be no difference between the almond sample percentage and the almond population percentage.

Answer 1

Let's analyze the information and statements presented in your question.

(a) Percent Bar Graph for Mixed Nuts

First, let's calculate the population percentages for almonds and cashews in the container of mixed nuts.

• Total mixed nuts: 7500
• Almonds: 5475
• Cashews: 2025

The percentages can be calculated as follows:

• Almonds percentage: \[ \text{Almonds percentage} = \left(\frac{5475}{7500}\right) \times 100 \approx 73% \]

• Cashews percentage: \[ \text{Cashews percentage} = \left(\frac{2025}{7500}\right) \times 100 \approx 27% \]

Percent Bar Graph

The percent bar graph would show approximately 73% for almonds and 27% for cashews.

(b) Assessment of Statements

Now, let's evaluate the statements based on what we know.

1. Statement: "In any random sample of 125 mixed nuts, the almond sample percentage must always be equal to the almond population percentage."

   • True/False: False. The almond sample percentage can vary because samples are taken at random. They are expected to approximate the population percentage, but they do not have to equal it exactly.

2. Statement: "In any random sample of 125 mixed nuts, the almond sample percentage is always 50%."

   • True/False: False. From the population percentages calculated earlier, we see the almond population percentage is about 73%. There is no reason the sample percentage would be consistently 50%; it varies based on randomness.

3. Statement: "With a very large sample size, there must be no difference between the almond sample percentage and the almond population percentage."

   • True/False: False. While larger samples tend to yield estimates that are closer to the population parameters (due to the law of large numbers), there can still be sampling variability. However, the difference is generally expected to be smaller with larger samples.

Summary

• For part (a), you would construct a percent bar graph showing almonds as approximately 73% and cashews as approximately 27%.
• In part (b), all the statements are False.