## Confidence Intervals for a Proportion

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Show

50 100 250
90 95 99
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### Instructions

Confidence Intervals Applet Activity

Applet Overview: The large ‘jar’ contains 10,000 blue and orange balls. What proportion of the balls are blue?

To know the true proportion of blue balls, it would be necessary to count all the blue balls in the large jar. A large population like this one is often inaccessible due to constraints of time and other resources. Instead, choose a (much smaller) sample from the jar, compute the proportion of blue balls in the sample, and use that to estimate the proportion of blue balls in the whole population.

Buttons:

• Sample – Use this button to choose a single sample from the large jar. The sample will appear in the small jar and a confidence interval for the proportion of blue balls in the sample is drawn on the plot below. Repeat this process to draw more samples.
• Sample 100 – This button will cause the applet to choose 100 samples from the large jar in rapid succession. Only the last of the 100 will be shown in the sample jar. Confidence intervals for the proportions of blue balls observed the samples are plotted on the graph below.
• Clear plot – This button erases the graph and empties the sample jar but does not change the population. Use this button when you want to look at confidence intervals based on a new sample size.
• New Population – This button clears the plot, empties the sample jar, and fills the large jar with a new population of balls.

Other components:

• Show p check box – Use this box to show the value of the parameter, that is, the true proportion of blue balls in the population (large jar). The proportion is displayed beside the check box and is indicated in the plot.
• Sample size radio buttons – Use the radio buttons to set the size of the sample: 50, 100 (default), or 250 balls.
• Confidence radio buttons – The radio buttons can be used to set the confidence level to 90, 95 (default), or 99.