Decrease Confidence Level Compensate Increased Margin Error
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Sample Size And Confidence Interval Relationship
RELATED ARTICLES How Sample Size Affects the Margin of Error Statistics Essentials For Dummies Statistics For Dummies,
What Happens To The Confidence Interval If You Increase The Margin Of Error
2nd Edition SPSS Statistics for Dummies, 3rd Edition Statistics II for Dummies Load more EducationMathStatisticsHow Sample Size Affects the Margin of Error How Sample Size Affects the Margin
What Happens To The Confidence Interval If You Increase The Sample Size
of Error Related Book Statistics For Dummies, 2nd Edition By Deborah J. Rumsey In statistics, the two most important ideas regarding sample size and margin of error are, first, sample size and margin of error have an inverse relationship; and second, after a point, increasing the sample size beyond what you already have gives you a diminished how does sample size effect confidence interval return because the increased accuracy will be negligible. The relationship between margin of error and sample size is simple: As the sample size increases, the margin of error decreases. This relationship is called an inverse because the two move in opposite directions. If you think about it, it makes sense that the more information you have, the more accurate your results are going to be (in other words, the smaller your margin of error will get). (That assumes, of course, that the data were collected and handled properly.) Suppose that the Gallup Organization's latest poll sampled 1,000 people from the United States, and the results show that 520 people (52%) think the president is doing a good job, compared to 48% who don't think so. First, assume you want a 95% level of confidence, so you find z* using the following table. z*-Values for Selected (Percentage) Confidence Levels Percentage Confidence z*-Value 80 1.28 90 1.645 95 1.96 98 2.33 99 2.58 From the table, you find
Explore My list Advice Scholarships RENT/BUY SELL MY BOOKS STUDY HOME TEXTBOOK SOLUTIONS EXPERT Q&A TEST PREP HOME ACT PREP SAT PREP PRICING ACT what will reduce the width of a confidence interval pricing SAT pricing INTERNSHIPS & JOBS CAREER PROFILES ADVICE EXPLORE MY LIST narrow confidence interval ADVICE SCHOLARSHIPS Chegg home Books Study Tutors Test Prep Internships Colleges Home home / study / math / statistics confidence interval width and probability / questions and answers / (i already have the answers written in just checking ... Question: (I already have the answers written in just checki... (I already have the answers http://www.dummies.com/education/math/statistics/how-sample-size-affects-the-margin-of-error/ written in just checking if correct before I submit it) Internet company Gurgle is carrying out testing on the efficiency of its search engine. A sample of 40 searches have been carried out and the time taken to display the results has been recorded for each search. The mean search time for the sample was calculated as 0.1171 seconds. The standard deviation of http://www.chegg.com/homework-help/questions-and-answers/already-answers-written-checking-correct-submit-internet-company-gurgle-carrying-testing-e-q6823733 the search times for the sample was calculated as 0.0162 seconds. The population standard deviation of search times is unknown. a)Select all the techniques that are commonly used to construct a confidence interval for the mean when the population standard deviation (?) is unknown: Approximate the population standard deviation (?) with the sample standard deviation (s) Replace the sample size (n) with n-1 Decrease the confidence level to compensate for the increased margin of error Approximate the standard normal distribution with the Student's t distribution b)Calculate the upper and lower bounds of the 95% confidence interval for the mean search time for the Gurgle search engine. You may find this Student's t distribution table useful. Give your answers in seconds to 4 decimal places. Upper bound = 0.2223 seconds Lower bound = 0.1119 seconds Expert Answer Get this answer with Chegg Study View this answer OR Find your book Find your book Need an extra hand? Browse hundreds of Statistics and Probability tutors. ABOUT CHEGG Media Center College Marketing Privacy Policy Your CA Privacy Rights Terms of Use General Policies Intellectual Property Rights Investor Relations Enrollment
95% confidence interval: = (94.32 minutes , 125.68 minutes) b) No! That’s NOT what a confidence interval for the mean means. What it does mean is that we are http://oregonstate.edu/instruct/st351/kollath/solutions/chap6.htm 95% confident that the mean number of minutes per week spent study statistics for the population of ALL students in the introductory course is between 94.32 minutes and 125.68 minutes. 6.5 a) = $20 b) $40 (two standard deviations is $40) c) $40 (again, within two standard deviations, which is $40) 6.7: a) First, you need to calculate the sample mean: = 123.8 bushels per acre (approximately) confidence interval we’re given: n = 15, = 10 bushels per acre, and z* = 1.645 (for a 90% confidence level) 90% confidence interval: = (119.6 bushels/acre , 128.0 bushels/acre) b) z* = 1.96 (for 95% confidence level) 95% confidence interval: = (118.7 bushels/acre , 128.9 bushels/acre) c) z* = 2.576 (for 99% confidence level) 99% confidence interval: = (117.1 bushels/acre , 130.5 bushels/acre) d) As what happens to the level of confidence increases, the margin of error increases. 6.14: For a 95% confidence interval, you would expect 95% of all confidence intervals constructed from samples of size n from the same population to contain the population mean. 6.15: Same as 6.14 except you’d expect 80% of all confidence intervals constructed from samples of size n from the same population to contain the population mean. 6.19: a) z* = 1.96 (for 95% confidence level), n = 100, = 12. margin of error = = 2.352 b) margin of error = = 7.438 c) Find n such that m (margin of error) = 3 for a 95% confidence interval. = 61.47. Round up: n = 62. 6.23: a) No. We’re 95% sure (or confident) that the true population percent falls in this interval, but not 100% certain. b) Answers will vary. But, it should be something like: this interval will contain the true percentage in the population 95% of the time. c) Since the margin of error (m) = and z* = 1.96 and m = 3%, then 3 = (1.96)(). Therefore, = 3 / 1.96 = 1.53% d) No! The margin of error accounts for random fluctu