Question

Leandro wants to estimate the proportion of light bulbs that arrive broken upon shipment to his store. he takes a random sample of \[500\] bulbs and finds that \[25\] arrived broken. he's willing to assume independence between bulbs in the sample. based on this sample, which of the following is a \[90\%\] confidence interval for the proportion of bulbs that arrive broken?

a) 0.05±1.645√0.05(0.95)/500
b) 0.05±1.96√0.05(0.95)/500
c) 25±1.645√25(475)/500
d) 25±1.96√25(475)/500

Answer 1

The correct 90% confidence interval for the proportion of light bulbs that arrive broken is option a), which is calculated using the sample proportion, z-score for the confidence level, and the sample size. option A is correct answer.

Step-by-step explanation:

Leandro is looking at estimating the proportion of light bulbs that arrive broken upon shipment to his store. He takes a random sample of 500 bulbs and finds that 25 arrived broken. To calculate a 90% confidence interval for the proportion of bulbs that arrive broken, the sample proportion (p) is 25/500 which is 0.05. For a 90% confidence level, the z-score is 1.645.

The formula for the confidence interval is given by:

p ± z * sqrt((p*(1-p))/n)

Plugging the values into the formula, we get:

0.05 ± 1.645 * sqrt((0.05*(1-0.05))/500)

So, the correct answer for the 90% confidence interval for the proportion of bulbs that arrive broken is:

a) 0.05±1.645√0.05(0.95)/500