6.16 More confidence interval mistakes and misunderstandings. Suppose that 100 randomly selected members of the Karaoke Channel were asked how much time they typically spend on the site during the week. The sample mean was found to be 3.8 hours. Assume that the population standard deviation is known to be o = 2.9. (a) Cary Oakey computes the 95% confidence interval for the average time on the site as 3.8 ± 1.96(2.9/100). What is his mistake? (b) He corrects this mistake and then states that "95% of the members spend between 3.23 and 4.37 hours a week on the site." What is wrong with his interpretation of this interval? (c) The margin of error is slightly larger than half an hour. To reduce this to roughly 15 minutes, Cary says that the sample size needs to be doubled to 200. What is wrong with this statement?

6.16 More confidence interval mistakes and misunderstandings. Suppose that 100 randomly selected members of the Karaoke Channel were asked how much time they typically spend on the site during the week. The sample mean was found to be 3.8 hours. Assume that the population standard deviation is known to be o = 2.9. (a) Cary Oakey computes the 95% confidence interval for the average time on the site as 3.8 ± 1.96(2.9/100). What is his mistake? (b) He corrects this mistake and then states that "95% of the members spend between 3.23 and 4.37 hours a week on the site." What is wrong with his interpretation of this interval? (c) The margin of error is slightly larger than half an hour. To reduce this to roughly 15 minutes, Cary says that the sample size needs to be doubled to 200. What is wrong with this statement?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

MODULE 2 2. A sample of 20 bags of the same brand of candies was selected and found a mean weight of 120 grams. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The population standard deviation is known to be 2.1 grams. Construct a 90% confidence interval for the population mean weight of the candies. 3. A survey of 200 Internet users shows that they spend an average of 2 hours and 22 minutes per day on social networking. If the margin of error is 2.2 hours at 95% confidence, construct the confidence interval. 4. Suppose that a government law office does a study to determine the time needed to complete one personal profile sheet for consultation. It randomly surveys 100 people. The sample mean is 23.6 minutes. There is a known standard deviation of 7.0 minutes. The population distribution is assumed to be normal. Construct a 95% confidence interval for the population mean to complete the form. 5. A camp counselor is interested…
53.305) B. (24.591, 35.563) C. (26.591, 37.563) D. (28.591, 39.563) 34. A simple random sample of size n = 36 is taken from a normally distributed original population. The sample standard deviation iss = 7. Find the 99% confidence interval for the population variance o2. A. (27.453, 98.756) B. (28.453, 99.756) C. (29.453, 100.756) D. (30.453, 101.756)
23. A sample of 8 female college students consumes an average of 10 liters of alcohol per month, with a sample standard deviation of 3.9 liters. Monthly alcohol consumption is Normally distributed. Which of the options below is the 95% Confidence Interval for the mean? Group of answer choices 7.69 to 12.31 8.04 to 11.96 6.74 to 13.26 8.11 to 11.89
selected parts. The sample standard deviation is s =0.37. Construct a 95% two-sided confidence interval for the standard deviation 5. The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. a. After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 90% confidence interval for the mean assembly time. b. How many workers should be involved in this study in order to have the mean assembly time estimated up to + 15 seconds with 90% confidence? 6. A new rocket-launching system is being considered for deployment of small, short-range rockets. The existing system has p = 0.8 as the probability of a successful launch. A sample of 40 experimental launches is made with the new system, and 34 are successful. Using 95% O Focus English (United States) search…
8. Form a 90% confidence interval on the difference in means. group wine sample std dev 2.0 mean 10 17.4 no alcohol 10 12.4 2.0
Suppose you work for the Department of Environment and National Resources (DENR). You want to estimate, with 95% confidence, the mean length of all tilapia in a fish hatchery pond. You take a random sample of 10 tilapia and determine the average length is 10.5 inches and the sample standard deviation is 2.9 inches. Construct a confidence interval for this sample and interpret the result.
Suppose a randomly selected sample of n = 69 men has a mean foot length of x = 28.3 cm, and the standard deviation of the sample is 3 cm. Calculate an approximate 95% confidence interval for the mean foot length of men. (Round the answers to one decimal place.) to cm
4. 5. A sample of 26 Chips Ahoy regular cookies is taken by a Nabisco quality control manager, and it is found that the mean number of chocolate chips per cookie is 20.39. Nabisco knows that the standard deviation, o, is 2.55 for these cookies. Use your calculator to build a 98% confidence interval for the real mean number of chocolate chips per cookie. Then write a sentence or two that interprets your confidence interval. A researcher is collecting data about the SEC (Southeastern Conference) and its student-athletes. If the researcher wants to estimate the mean number of hours spent on required athletic activities by all student-athletes in the conference, then how many student-athletes must be included in the sample to be 98% confident that the sample mean is within 0.4 hour of the population mean? Assume the population standard deviation (o) is 2.41. Use the formula and show all work. 5.
Q3. A business man want to decide about the hair-cut prices and so he decided to know the mean time spet on hair-cuts. He has no record of time needed for hair-cut. He wanted a max error of +0.2. He took a sample of size 30 and found that s= 1.5 min. Find the sample size needed to achieve the 95% confidence level.
Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 4 inches. The heights of 9 randomly selected students are 72, 61, 65, 64, 61, 67, 71, 63 and 72. x¯ =? Margin of error at 90% confidence level =? 90% confidence interval = [__.__ , __.__]
A researcher is conducting a study to determine the mean trough dosage of medication for a population. Assume a previous study was conducted for the same medication and the mean trough dose was found to be 490 mg with a standard deviation of 30 mg. If the researcher wants to be 95% confident the true mean trough dosage of the medication is within 10 mg of the true mean trough dosage, what sample size is needed if the study is predicted to have an 76% retention rate? n = 50 n = 71 n = 47 n = 104
The mayor is interested in finding a 90% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 185 residents whose mean number of pounds of trash generated per person per week was 34.3 pounds and the standard deviation was 6.4 pounds. Round answers to 3 decimal places where possible. a. With 90% confidence the population mean number of pounds per person per week is between and pounds. b. If many groups of 185 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about percent will not contain the true population mean number of pounds of trash generated per person per week.