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Construct a 99% confidence interval for the following data set. n = 1,500 q-hat = 0.48

User Jloubert
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Final answer:

To construct a 99% confidence interval for the given data set, we need to calculate the margin of error using the formula and find the critical value for a 99% confidence level. Then, we can calculate the confidence interval by subtracting and adding the margin of error to the estimated proportion.

Step-by-step explanation:

To construct a 99% confidence interval, we need to find the margin of error (EBP), which is calculated using the formula EBP = z * sqrt((p' * q') / n). Here, n = 1,500 and q-hat = 0.48. Since the sample size is large (>30) and both np' and nq' are greater than 5, we can use the normal approximation to find the critical value z for 99% confidence level.

Using a calculator or a Z-table, the critical value z corresponding to a 99% confidence level is approximately 2.58. Now we can plug in the values into the formula to calculate the margin of error:

EBP = 2.58 * sqrt((0.48 * 0.52) / 1500) = 0.022

The 99% confidence interval can be calculated as (p' - EBP, p' + EBP). Plugging in the values, we get (0.48 - 0.022, 0.48 + 0.022) = (0.458, 0.502)

User Radkovo
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