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WHAT IS A CONFIDENCE INTERVAL ANYWAY?
Objective: We will construct confidence intervals using simulation and learn how to interpret the results.
Activity:
Conduct the following experiment with 40 people. Have each person hold both hands out in front of them, cupping their hands to make a small opening. Focus on some distant object, and close each eye. The eye which can still see the object through the opening is the dominant eye. What proportion of the sample is righteye dominant?
In this next part, you will be taking samples from a population in which 40% have some characteristic in order to see how close the proportions in the samples tend to come to 40%.
Use your calculator to simulate taking a sample size of 40 from a population with 40% successes. Use the randInt(0, 9, 40) function. Let the digits 0, 1, 2, 3 represent a success and 4, 5, 6, 7, 8, 9 represent a failure. Place a tally mark in the table on the next page.
Combine your results with other members of your class, repeating the simulation until the class has placed tally marks from 100 different samples in the frequency column of the table.
Comparing your proportion from #1 to the frequency table on the next page, is it plausible (has a reasonable chance of being the case) that 40% of the population are righteye dominant? Explain.
Complete the following sentences based on your table on the next page. Less than 5% of the time, there were ________ successes or fewer. Less than 5% of the time, there were________ successes or more.
Number of SuccessesFrequency012345678910111213141516171819202122232425262728293031323334353637383940Total100
On the chart below, draw a thin horizontal box aligned with the 40% "Percentage of Successes in Population" on each side. Using "Number of Success in Sample" on the bottom as a guide, the box should stretch in length between your two answers to step d.
About 40% of Americans aged 19 to 28 claim that they have used an illicit drug other than marijuana. If a random sample of 40 Americans aged 19 to 28 finds 25 who claim to have used an illicit drug other than marijuana, would you be surprised? Explain.
According to the U.S. Bureau of Labor Statistics, about 40% of women with children under the age of 6 do not participate in the labor force. Would it be plausible for a survey of 40 randomly chosen mothers of children under the age of 6 to find that 12 are not working? Explain.
The class should now divide into smaller groups. Each group will be given one of the percentages on the sides of the chart on the previous page. With your group, repeat steps a, b, d, and e for your new percentage.
Number of SuccessesFrequency012345678910111213141516171819202122232425262728293031323334353637383940Total100
Use the completed chart on page 3 to answer these questions.
According to the U.S. Census, about 30% of people aged 25 to 44 live alone. In a random sample of 40 people aged 25 to 44, would it be plausible to get 20 who live alone?
We select a random sample of size 40 and get a sample proportion of 0.90 successes. Is the sample plausible if the population has 75% successes?
According to the 1990 U.S. Census, about 80% of men aged 20 to 24 have never been married. In a random sample of 40 men aged 20 to 24, how many unmarried men is it plausible to get? What proportion of unmarried men is it plausible to get?
Suppose you flip a coin 40 times; how many heads is it plausible to get?
In the 1992 presidential election, Bill Clinton got 43% of the vote. In a random sample of 40 voters, what is the largest proportion of people who voted for Clinton that it is plausible to get? The smallest?
Based on your chart your class has completed, is it plausible that 60% is the percentage of the population that are righteye dominant? What percentages are plausible? These percentages are called the 90% confidence interval.
Use your completed chart to find these confidence intervals.
Suppose that a random sample of 40 toddlers finds that 34 know what color Barney is. What is the 90% confidence interval for the percentage of toddlers who know what color Barney is?
Suppose that a random sample of 40 adults finds that 10 know what color Barney is. What is the 90% confidence interval for the percentage of adults who know what color Barney is?
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