Question

1messageLeo wants to build a confidence interval with 98% confidence 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.What critical value should Leo use to construct this confidence interval?z* = 1.96z* = 1.280z* = 2.326z* = 1.645z* = 2.576

Answer 1

To find the critical value that Leo should use, we proceed as follows:

- We find the p value, which is:

p = 25/500 = 0.05

-Next we use the p value to find the alpha value:

alpha = 2 * p = 2 * 0.05

alpha= 0.10

Therefore, the confidence interval that Leo should use is:

1 -0.10 = 0.90 = 90%

Now, for a 90% confidence interval, from the t -tables, the appropriate critical value is 1.645

Thus: z* = 1.645