BackA technician wants to estimate the average battery life of a new type of smart phone, so he tests 8 randomly selected phones & records the data below. Assuming battery life has a normal dist, make a 90% conf. int. for the mean battery life.
In Exercises 5–8, (a) identify the critical value ta/2 used for finding the margin of error, (b) find the margin of error, (c) find the confidence interval estimate of u, and (d) write a brief statement that interprets the confidence interval.
Birth Weights Here are summary statistics for randomly selected weights of newborn girls: n=36, x=3150.0g, s=695.5g (based on Data Set 6 “Births” in Appendix B). Use a confidence level of 95%.
In Exercises 7 and 8, find the margin of error for the values of c, s, and n.
c = 0.99, s = 3, n = 6
In Exercises 21–24, construct the indicated confidence interval for the population mean μ.
c = 0.95, xbar = 31.39, σ = 0.80, n = 82.
The data set represents the scores of 12 randomly selected students on the SAT Physics Subject Test. Assume the population test scores are normally distributed and the population standard deviation is 108. (Adapted from The College Board)
b. Construct a 90% confidence interval for the population mean. Interpret the results.
In Exercises 29–32, determine the minimum sample size n needed to estimate for the values of c, σ, and E.
c = 0.95, σ = 2.5, E = 1.
When all other quantities remain the same, how does the indicated change affect the width of a confidence interval? Explain.
a. Increase in the level of confidence
In Exercises 9–12, construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.
c = 0.98, xbar = 4.3, s = 0.34, n = 14
Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics.
c = 0.88
The data set represents the amounts of time (in minutes) spent checking email for a random sample of employees at a company.
c. Repeat part (b), assuming σ = 3.5 minutes. Compare the results.
[APPLET] The winning times (in hours) for a sample of 20 randomly selected Boston Marathon Women’s Open Division champions from 1980 to 2019 are shown in the table at the left. Assume the population standard deviation is 0.068 hour. (Source: Boston Athletic Association)
a. Find the point estimate of the population mean.
Determine the minimum sample size required to be 99% confident that the sample mean driving distance to work is within 2 miles of the population mean driving distance to work. Use the population standard deviation from Exercise 2.
Cell Phone Radiation Here is a sample of measured radiation emissions (cW/kg) for cell phones (based on data from the Environmental Working Group): 38, 55, 86, 145. Here are ten bootstrap samples:
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a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the population mean.
Repeat Exercise 26 for samples of size 72 and 108. What happens to the mean and the standard deviation of the distribution of sample means as the sample size increases?
In Exercises 13 and 14, use the confidence interval to find the margin of error and the sample mean.
(14.7, 22.1)