Exam2_A_F18_Key.pdf

# A 4pts using dawns data construct a 96 confidence

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(a) [4pts.] Using Dawn’s data, construct a 96% confidence interval for the mean weight of all Magikarp in Pok´ emon GO. Show all your work, report the critical value, and round your final answers to 2 decimal places. Form A: 9 . 647 ± 2 . 147 2 . 568 36 = (8.73 , 10.57) where t * 35 = t * 30 = 2 . 147 Form B: 10 . 092 ± 1 . 648 2 . 349 49 = (9.53 , 10.66) where t * 48 = t * 40 = 1 . 684 (b) [4pts.] For each of following situations, determine whether the width of the confidence interval from question (2a) will increase, decrease, or be unchanged. For each of these situations, assume all other quantities remain as given in question (2a). Circle the correct answer for each scenario. Form A: increase decrease decrease decrease Form B: increase increase increase decrease i. A sample standard deviation of 3 kg. increase decrease unchanged ii. A sample size of 52. increase decrease unchanged iii. A confidence level of 90%. increase decrease unchanged iv. Knowing that the population variance is increase decrease unchanged the same as the sample variance. -score:

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Exam II Stat 226 Fall 2018 – FORM A : KEY Page 5 (c) A team of data-miners was able to get some information from Niantic’s servers. They found out that all Magikarp weights follow a normal distribution with a mean of 10 kg. i. [2pts.] This fact tells us something about one of our population parameters. Identify the name of the parameter and its value. Population mean ( μ ) = 10 kg ii. [2pts.] The data-miners computed a 90% confidence interval for the mean to be 8.92 to 10.37 kg. Does this interval agree with what we currently know about the population mean? Briefly explain. Yes, 10 kg is within the 96% CI. (d) [3pts.] Besides the population mean weight for Magikarp, the data-miners also found that the population standard deviation σ = 2 . 5 kg and that a Magikarp is considered big if its weight is greater than 13 kg. Based on this information, what is the probability that the next Magikarp caught by Dawn is big ? Show all your work for full credit. Form A: P ( X > 13) = P ( Z > 13 - 10 2 . 5 ) = P ( Z > 1 . 2) = 1 - 0 . 8849 = 0 . 1151 Form B: P ( X > 14) = P ( Z > 14 - 10 2 . 5 ) = P ( Z > 1 . 6) = 1 - 0 . 9452 = 0 . 0548 (e) [3pts.] During a late night outing, Dawn’s phone died and she lost the data she previously collected. She goes on to record the weight of another 36 Magikarps she caught, and constructed a new 96% confidence interval. What will NOT change from the interval in (2a)? (circle all that apply): Form A: iii vi viii Form B: i iv viii i. The standard error ( s n ). ii. The value of the sample standard deviation ( s ). iii. The value of the population mean ( μ ). iv. The lower and upper bound of the confidence interval. v. The center of the confidence interval. vi. The t -critical value ( t * , or t α/ 2 , 35 ). vii. The sample mean (¯ x ). viii. The value of the population standard deviation ( σ ). MAX=10
Exam II Stat 226 Fall 2018 – FORM A : KEY Page 6 3. Professors’ Salary. Indeed.com is an employment-related search engine which provides services such as job searches, job trends, resume upload, industry trends and salary information. According to Indeed.com , the average salary of assistant professors at U.S. universities is \$78,000. A large university, skeptical of the information provided by Indeed.com , hires a group of consultants and asks them to check Indeed.com ’s claim. The consulting group collects information on 50 randomly

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• Spring '08
• ABBEY
• Statistical hypothesis testing

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