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Now suppose we took 200 random samples of 100 college students and constructed a 95% confidence interval for each one. The picture below illustrates a
Now suppose we took 200 random samples of 100 college students and constructed a 95% confidence interval for each one. The picture below illustrates a simulated result of this situation (i.e., 200 confidence intervals constructed from our 200 random samples). 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Population Proportion pPa rt A: The red lines in the previous picture represent the confidence intervals that did not contain the population proportion 0.40. Out ofthe 200 confidence intervals. hov.r many ofthern did not contain the population proportion 0.40? Hint The red lines are those that did not contain the population proportionhow many red lines are in the previous picture? It might be easier to count the red squares to identify the number of confidence intervals that did not contain the population proportion. Pa rt B: Given your answer to the previous question and knowing there are 200 total condence intervals. how many confidence intervals from this simulated result did contain the population proportion? Hint Subtract the value you calculated in Part A from 200 to identify the remaining number of intervals that did contain the population proportion. Pa rt C: Given your previous answers, what proportion of the 200 confidence intervals did contain the population proportion 0.40? What is this value as a percentage? Hint In Part B. you calculated the number of intervals containing the proportion [1.40. Divide this value by 200 to calculate the proportion. i|r|i :% ofthe intervals
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