Section 9.2 HW
Determine the point estimate of the population mean and margin of error for the confidence interval. Lower bound is 18, upper bound is 26.
22; 4; Margin of error: Mean-Lower bound
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3 points with 99% confidence assuming s=11.3 based on earlier studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required?
95; 39; Decreasing the confidence level decreases the sample size needed. ((critical value x s)/points)^2
To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.
False
A trade magazine routinely checks the drive-through service times of fast-food restaurants. An 80% confidence interval that results from examining 563 customers in one fast-food chain's drive-through has a lower bound of 165.6 seconds and an upper bound of 168.8 seconds. What does this mean?
One can be 80% confident that the mean drive-through service time of this fast-food chain is between 165.6 seconds and 168.8 seconds.
A survey was conducted that asked 1004 people how many books they had read in the past year. Results indicated that x =10.3 books and s=16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval
There is 90% confidence that the population mean number of books read is between 9.44 and 11.16 x(+/-) 0.86
(a) Find the t-value such that the area in the right tail is 0.05 with 9 degrees of freedom. (b) Find the t-value such that the area in the right tail is 0.01 with 24 degrees of freedom. c) Find the t-value such that the area left of the t-value is 0.25 with 16 degrees of freedom. [Hint: Use symmetry.] (d) Find the critical t-value that corresponds to 80% confidence. Assume 24 degrees of freedom.
a) 1.833 (y=9, x=0.05) b) 2.492 c) -0.69 d) 1.318
In a survey, 1000 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for mean number of hours worked was lower bound: 38.8 and upper bound: 41.6. Which of the following represents a reasonable interpretation of the result? a) There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 38.8 hours and 41.6 hours. b) We are 95% confident that the mean number of hours worked by adults in this country in the previous week was between 38.8 hours and 41.6 hours. c) 95% of adults in this country worked between 38.8 hours and 41.6 hours last week (d) We are 95% confident that the mean number of hours worked by adults in a particular area of this country in the previous week was between 38.8 hours and 41.6 hours.
a) Flawed. This interpretation implies that the population mean varies rather than the interval b) Correct. This interpretation is reasonable. c) Flawed. This interpretation makes an implication about individuals rather than the mean. d) Flawed. The interpretation should be about the mean number of hours worked by adults in the whole country, not about adults in the particular area.
