Question

Question 4

A company has developed a new type of light bulb, and wants to estimate its mean lifetime. A simple random sample of 12 bulbs had a sample mean lifetime of 651 hours with a sample standard deviation of 43 hours. It is reasonable to believe that the population is approximately normal. Find the lower bound of the 95% confidence interval for the population mean lifetime of all bulbs manufactured by this new process.

Round to the nearest integer. Write only a number as your answer. Do not write any units.

Question 5

A random sample of 40 videos posted to YouTube was selected. A month later, the number of times that each had been viewed was tabulated. The mean number of viewings was 143 with a sample standard deviation of 559 . Find the upper bound of the 99% confidence interval for the mean number of times videos posted to YouTube have been viewed in the first month.

Round to the nearest integer. Write only a number as your answer. Do not write any units.

Question 10

A researcher wants to construct a 99% confidence interval for the proportion of people who changed jobs in the past year. What sample size is needed so that the confidence interval will have a margin of error of 0.049 ?

Answer 1

Answer

(4) Using TI 84 calculator

press stat then tests then Tinterval

enter the data

xbar = 651

s = 43

n =12

c-level = 0.95

press calculate

we get

Lower bound = 624

(5)

Using TI 84 calculator

press stat then tests then Tinterval

enter the data

xbar =143

s = 559

n =40

c-level = 0.99

press calculate

we get

Upper bound =382

(10) sample size n = 0.25*(z/E)^2

where z = 2.58 (for 99% confidence level using z table)

E = 0.049 (margin of error)

this implies

sample size n = 0.25*(2.58/0.049)^2

= 0.25*2772.345

= 693.09

= 693 (nearest integer) or 694 (next integer)