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GBS 221: Business Statistics CHAPTER 8 with solutions/answers Homework All answers correct!!! 1) A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is σ = 5. a. What is the standard error of the mean, σX ? (to 2 decimals) b. At 95% confidence, what is the margin of error? (to 2 decimals) a) σ / √n 5/ √40 = .7905 =.79 b) at 95% of the values of any normally distributed random variable are within ± 1.96 standard deviations from the mean 1.96 * .79 =1.5484 round up… =1.55 2) A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ = 15. a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place. Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places. c. What is the effect of a larger sample size on the interval estimate? Larger sample provides a - Select your answer –larger/smallerItem 3 margin of error. a) So the sample mean is 80 15/ √60 = 1.936 1.936 * 1.96 = 3.7955 1.96 comes from 95% probability 80 ± 3.79 =(76.2,83.8) =(76.2,83.8) b) c) Smaller 3) The Wall Street Journal reported that automobile crashes cost the United States \$162 billion annually ( The Wall Street Journal , March 5, 2008). The average cost per person for crashes in the Tampa, Florida, area was reported to be \$1599. Suppose this average cost was based on a sample of 40 persons who had been involved in car crashes and that the population standard deviation is σ = \$650. A) What is the margin of error for a 95% confidence interval? Round your answer to two decimal places. 650/√40 =102.774024 102.774024 * 1.96 =201.437087
=201.44 4) AARP reported on a study conducted to learn how long it takes individuals to prepare their federal income tax return ( AARP Bulletin , April 2008). The data contained in the WEBfile named TaxReturn are consistent with the study results. These data provide the time in hours required for 40 individuals to complete their federal income tax returns. Using past years' data, the population standard deviation can be assumed known with σ = 11 hours. What is the 95% confidence interval estimate of the mean time it takes an individual to complete a federal income tax return? Round your answer to one decimal place. Mean = 33.495 11/ √40 = 1.739 1.739 * 1.96 = 3.408 33.495 ± 3.408 = 30.1 to 36.9 = 30.1 to 36.9 5) For a t distribution with 16 degrees of freedom, find the area, or probability, in each region. (to 2 decimals) a. To the right of 2.120 .025 b. To the left of 1.337 .9 c. To the left of -1.746 .05 d. To the right of 2.583 .01 e. Between -2.120 and 2.120 .95 f. Between -1.746 and 1.746 .9 6) The following sample data are from a normal population: 10, 8, 12, 16, 13, 11, 6, 4.

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