Question

Construct a 90% confidence interval of the population proportion using the given information. x=75n = 150 , The lower bound is The upper bound is (Round to three decimal places as needed) Enter your answer

Answer 1

To construct a 90% confidence interval for a population proportion, you can use the formula (p' - EBP, p' + EBP), where p' is the sample proportion and EBP is the error bound. In this case, with x = 75 and n = 150, the confidence interval is (0.430, 0.570).

Step-by-step explanation:

To construct a 90% confidence interval for a population proportion, we can use the formula:

(p' - EBP, p' + EBP)

where p' is the sample proportion, EBP is the error bound for the population proportion, and EBP is calculated using the formula:

EBP = Z * sqrt((p' * q') / n)

In this case, x = 75, n = 150, and we need to find the error bound for a 90% confidence interval.

First, we need to find p', which is the sample proportion:

p' = x / n = 75 / 150 = 0.5

Next, we need to find q' (1 - p'):

q' = 1 - p' = 1 - 0.5 = 0.5

Now, we can calculate the error bound EBP:

EBP = Z * sqrt((p' * q') / n)

Since the confidence level is 90%, we can determine the Z value using a standard normal distribution table or a calculator. The Z value for a 90% confidence level is approximately 1.645.

Now we can plug in the values

EBP = 1.645 * sqrt((0.5 * 0.5) / 150) = 0.070

Finally, we can construct the confidence interval:

(p' - EBP, p' + EBP) = (0.5 - 0.070, 0.5 + 0.070) = (0.430, 0.570)