Question

Suppose that the lifetimes of light bulbs are approximately normally distributed. A random sample with 38 light bulbs was obtained with a mean of 60 hours and a standard deviation of 4.5 hours. With this information, answer the following questions.

1. To estimate the population mean, what is the Standard Error?
2. To estimate the population mean at 95% C.L., what is the Margin of Error?
3. At a 96% C.L., if the researcher wants to limit the margin of error within 0.5 hours, what size of the sample is needed?

The numbers of chocolate chips in a bag of chocolate chip cookies are approximately normally distributed. A random sample with 60 bags was obtained with a mean of 1200 chips and a standard deviation of 127 chips.

1. ​ To estimate the population mean, what will be the Standard Error of the estimation?
2. At a confidence level of 90%, what is the lower boundary of the estimation?
3. At a 92% C.L., if the researcher wants to limit the margin of error within 50 chips, what size of the sample is needed.

Answer 1

1. Standard error = S.D/√n = 4.5/√38 = 0.730

2. Margin of error = 1.96*0.730 = 1.431

.3.Margin of error for 96% cl = 0.5

So, 2.0537*4.5/√n = 0.5

Or, n= 342

4. Se = 127/√60 = 16.396

5.Lower bound of the 90% cl,

1200 - 1.645*16.396 = 1173.03

6. So here, 1.7507*127/√n = 50

Or, n= 20