Suppose that a random sample of 100 part-time college students is 68% female. In this activity, we calculate the 95% confidence interval for the proportion of all part-time college students that are female. Recall that the 95% confidence interval is: sample proportion ±± 2(SE) where SE is the standard error (or standard deviation). 1. First we need to find the standard error. In the previous module, we met the formula for calculating the standard deviation of the distribution of sampling proportions. SE=p(1−p)n−−−−−√SE=p(1−p)n But we don't know the population proportion, p. So to calculate the standard deviation (a.k.a. the standard error) we estimate the standard error with the sample proportion p^p^. SE≈p^(1−p^)n−−−−−√SE≈p^(1−p^)n In this scenario we are given that that a random sample of 100 part-time college students is 68% female. So the sample proportion of females is p^=0.68p^=0.68 and n=100n=100. Calculate the standard error. Round to three decimal places. 2. Recall that at 95% confidence level the margin of error is calculated as follows. margin of error = 2(SE). What is the margin of error? Do not round. 3. 95% confidence interval = sample proportion ±± margin of error Calculate the 95% confidence interval. What is the smallest number from the confidence interval? Enter your answer as a proportion (a decimal number) NOT a percentage. Do not round. 4. What is the largest number in your confidence interval? Enter your answer as a proportion (decimal number) NOT a percentage. If necessary, round to three decimal places. 5.State the confidence interval. Then convert the values to percentages and interpret the confidence interval in context.
Suppose that a random sample of 100 part-time college students is 68% female. In this activity, we calculate the 95% confidence interval for the proportion of all part-time college students that are female.
Recall that the 95% confidence interval is:
sample proportion ±± 2(SE) where SE is the standard error (or standard deviation).
1. First we need to find the standard error.
In the previous module, we met the formula for calculating the standard deviation of the distribution of sampling proportions.
SE=p(1−p)n−−−−−√SE=p(1−p)n
But we don't know the population proportion, p. So to calculate the standard deviation (a.k.a. the standard error) we estimate the standard error with the sample proportion p^p^.
SE≈p^(1−p^)n−−−−−√SE≈p^(1−p^)n
In this scenario we are given that that a random sample of 100 part-time college students is 68% female. So the sample proportion of females is p^=0.68p^=0.68 and n=100n=100.
Calculate the standard error. Round to three decimal places.
margin of error = 2(SE).
What is the margin of error? Do not round.
3. 95% confidence interval = sample proportion ±± margin of error
Calculate the 95% confidence interval.
What is the smallest number from the confidence interval? Enter your answer as a proportion (a decimal number) NOT a percentage. Do not round.
4. What is the largest number in your confidence interval? Enter your answer as a proportion (decimal number) NOT a percentage. If necessary, round to three decimal places.
5.State the confidence interval. Then convert the values to percentages and interpret the confidence interval in context.
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