Sample Size (All numerical answers should be integers * No decimals):
We would like to estimate the true mean amount of time (in minutes) Canadian teenagers spend on the internet per day. The population standard deviation of daily internet usage time is known to be 38 minutes.
(a) What sample size is required in order to estimate to within 15 minutes with 95% confidence? ____
(b) What sample size is required in order to estimate to within 5 minutes with 95% confidence? _____
(c) For a fixed confidence level, when we decrease the desired margin of error to one third its original value, we require _____ times the sample size.
(d) What sample size is required in order to estimate to within 15 minutes with 98% confidence? _____
(e) For a fixed margin of error, when we increase the desired confidence level, what happens to the required sample size?
- The required sample size decreases.
OR
- The required sample size increases.
(f) The United States has ten times the population of Canada. Assuming equal standard deviations, how many American teenagers must be sampled in order to estimate the true mean amount of time American teenagers spend on the internet per day to within 15 minutes with 95% confidence? _____
Confidence Levels (Give all numerical answers to two decimal places):
An RCMP officer would like to estimate the true mean speed of all vehicles along a particular stretch of highway. She measures the speeds of a simple random sample of 40 vehicles and calculates a mean speed of 114.55 km/h. The population standard deviation of speeds is known to be 12.69 km/h.
(a) A 93% confidence interval for the true mean speed of all vehicles on the highway is
( ____ , ____ ).
(b) A 99% confidence interval for the true mean speed of all vehicles on this highway is
( ____ , _____ ).
(c) When the confidence level increases, the length of the confidence interval
- increases
OR
- decreases
d) A random variable X follows a normal distribution with standard deviation 18. A random sample of 24 individuals is selected from the population, and a confidence interval for is calculated to be (87.535, 106.465). The confidence level for this interval is ____%.