Questions:
Briefly explain how the width of a confidence interval decreases with an increase in the sample size. Give me an example.
1 Briefly explain how the width of a confidence interval decreases with a decrease in the confidence level. Give me an example.
2 According to a study done by Dr. Martha S. Linet and others, the mean duration of the recent headache was 8.2 hours for a sample of 5055 females aged 12 through 29. Assume that this sample represents the current population of all headaches for all females aged 12 through 29 and that the standard deviation for this sample is 2.4 hours. Make a 95% confidence interval for the mean duration of all headaches for all 12-to-29- year-old females. Do by hand and using The Plan-alyzer.
3.4 A sample of 12 observations was drawn from a population of size 100.
Calculate a 95% confidence interval around the average for this sample by hand. HINT: You will want to use the finite population correction factor for this problem as found on slides 57 and 58.
13 15 9 11 8 16 14 9 10 14 16 12 Section 7 Exercises
4.5 A company wants to estimate the mean net weight of its "Big Top Circus" cereal boxes. A sample of 16 such boxes produced the mean net weight of 31.98 ounces with a standard deviation of .26 ounces. Make a 95% confidence interval for the mean net weight of all boxes. Do by hand and using The Plan-alyzer.
5. Crate and Barrel Cataloger promises its customers that the products ordered will be mailed within 72 hours after an order is placed. The quality ontrol department at the company checks from time to time to see if this promise is fulfilled. Recently, the quality control department took a sample of 50 orders and found that 42 of them were mailed within 72 hours of the placement of the orders.
a) Construct a 95% confidence interval for the percentage of all orders that are mailed within 72 hours of their placement. Do by hand and sing The Plan-alyzer.
b) Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Discuss all possible
alternatives. Which of these alternatives is the best?
6. In virtual reality a person views a computer-generated scene that changes as if the viewer's body were in motion. Some individual experience unpleasant side effects from virtual reality, such as nausea, dizziness, or disorientation. In a recent study by Clare Tegan of Britain's Defense Research Agency, each of the 150 people included in the study spent 20 minutes wearing a head-mounted virtual reality system through which he or she explored a virtual environment consisting of a series of rooms.
Either during their time in the virtual environment or in the 10 minutes immediately afterward, 61% of these 150 persons suffered side effects.
Find the 95% confidence interval for the proportion of all virtual reality users who would suffer side effects. Do by hand and using The Planalyzer.
7. One of the major problems faced by department stores is a high percentage of returns. The manager of Macy's wanted to estimate the percentage of all sales that result in returns. A sample of 40 sales showed that 8 of them had products returned within the time allowed for returns.
a) Construct a 99% confidence interval for the percentage of all sales that result in returns. Do by hand and using The Plan-alyzer.
b) Do you think 99% confidence is appropriate in this case and if not what would be a more appropriate level of confidence to use?
8. According to a survey, the mean price of gasoline in the U.S. was $1.20 per gallon in 1995 and $1.10 per gallon in 1994 (Wow, don't you ish!) Suppose these means were based on random samples of 100 gas station for 1995 and 120 gas station for 1994. Also, assume that the sample standard deviations were $.11 for 1995 and $.10 for 1994.
Find a 90% confidence interval for the difference between the mean gasoline prices for 1995 and 1994. Do by hand and using The Planalyzer.
9. An insurance company wants to know if the average speed at which men drive cars is higher than that of women drivers. The company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 68 miles per hour with a standard deviation of 2.2 miles.
Another sample of 18 cars driven by women on the same highway gave a mean speed of 65 miles per hour with a standard deviation of 2.5 miles.
Assume that the speeds at which all men and all women drive cars on this highway are both known to be normally distributed. Construct a 99% confidence interval for the difference between the mean speeds of cars driven by all men and all women drivers on this highway. Do by hand and using The Plan-alyer.
10. In a Prevention magazine survey released in 2008, Princeton Survey Research Association examined the weight of children aged 3 to 17. According to this study, 24% of children in this age group were overweight in 2000, and 31% were considered overweight in 2008. Suppose that these percentages are based on random samples of 400 and 500 children in the given age group in 2000 and 2008, respectively. Conduct a 95% confidence interval for the difference between the portions of the overweight 3-to-17-year-olds in 2000 and 2008. Do by hand and using The Plan-alyzer
Attachment:- ASSIGNMENT.rar