1 Why is a 99% confidence interval wider than a 95% confidence interval?
2. A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?
3. You take a sample of 22 From a population of test scores, and the mean of your sample is 60. (a) you know the standard deviation of the population is 10. what is the 99% confidence interval on the population mean. (b) now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. what is the 99% confidence interval on the mean now?
4 You were interested and how long the average psychology major at your college studies per night, so you asked in Psychology Majors to tell you the amount they study. they told you the following times: 2, 1.5, 3,2,3.5,1,0.5,3,2,4. (a) find the 95% confidence interval for the population mean. (b) find the 90% interval on the population mean.
5 What is meant by the term "90% confident" when constructing a confidence interval for a mean?
a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval
b. if we took repeated samples, approximately 90% of the confidence intervals calculated from those samples wouldl contain the sample mean.
c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those sample would contain the true value of population mean
d. if we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.
6 Suppose that a committee is studying whether or not there is a waste of time in the judicial system. it is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. the committee randomly surveyed 81 people who recently served as jurors. sample mean wait time was 8 hours with a sample standard deviation of 4 hours.
a.
i. x=_______
ii. sx=_________
iii. n=_________
iv. n1=_________
b. Define the random variable X in words
c. which distribution should you use for this problem? explain your choice.
d. construct a 95% confidence interval for the population mean time wasted
i. State the confidence interval
ii. Sketch the graph
iii. calculate the error bound
e. explain in a complete sentence with the confidence interval means.
7. In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. assume the underline distribution is approximately normal.
a. which distribution should you use for this problem? explain your choice.
b. Define the random variable X in words
c. construct a 95% confidence interval for the population mean cost of a used car.
i. State the confidence interval
ii. sketch the graph
iii. calculate the error bound
d. explain what a "90% confidence interval" means for this study
8. A quality control specialist for a restaurant chain text a random sample of size 12 to check the amount of soda served in the 16 ounce serving size. the sample mean is 13.30 with a sample standard deviation of 1.55. assume the underlying population is normally distributed. What is the error bound?
a. 0.87
b. 1.98
c. 0.99
d. 1.74
9. On May 23rd 2013 Gallup reported that of the 1005 people surveyed, 76% of U.S. workers believe that they will continue working past retirement age. the confidence level for this study was reported at 95% with a +/ 3% margin of error.
a. determine the estimated proportion from the sample
b. determine the sample size
c. Identify CL and a
d. calculate the error bound based on the information provided
e. compare the error Bound in part D to the margin of error reported by Gallup. explain any differences between the values.
f. create a confidence interval for the results of the study
g. a reporter is covering the release of the study for a local news station. How should she explained the confidence interval to her audience?