For each problem, select the best response.
(a) Suppose you collect a SRS of size n from a population and from the data collected you computed a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?
A. Use a larger confidence level.
B. Nothing can guarantee absolutely that you will get a larger interval. One can only say the chance of obtaining a larger interval is 0.05.
C. Use a smaller confidence level.
D. Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger.
E. None of the above.
(b) A 95% confidence interval for the mean μ of a population is computed from a random sample and found to be 10±4. We may conclude
A. that there is a 95% probability that the true mean is 10 and a 95% chance the true margin of error is 4.
B. that there is a 95% probability that μ is between 6 and 14.
C. 95% of the population is between 6 and 14.
D. that if we took many, many additional samples and from each computed a 95% confidence interval for μ, approximately 95% of these intervals would contain μ.
E. All of the above.
How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Here are data from students doing a laboratory exercise:
|33,190 31,860 32,590 26,520 33,280|
|32,320 33,020 32,030 30,460 32,700|
|23,040 30,930 32,720 33,650 32,340|
24,050 30,170 31,300 28,730 31,920
Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 3000 pounds. Give a 99% confidence interval for the mean load required to pull the wood apart. ( )to ( ) lb.
A study of the career paths of hotel general managers sent questionnaires to an SRS of 280 hotels belonging to major U.S. hotel chains. There were 169 responses. The average time these 169 general managers had spent with their current company was 9.98 years. (Take it as known that the standard deviation of time with the company for all general managers is 1.9 years.)
(a) Find the margin of error for an 85% confidence interval to estimate the mean time a general manager had spent with their current company: ( )years
(b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: ( ) years
(c) In general, increasing the confidence level ( ) the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)
A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 263 students wasx⎯⎯= 143 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviationσ= 65 minutes in the population of all first-year students at this university.
Use the survey result to give a 95% confidence interval for the mean study time of all first-year students. ( )to( ) .
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