A. A writing placement exam is given to test takers across the U.S.A sample of 1

Question

A. A writing placement exam is given to test takers across the U.S.A sample of 100 test takers has a mean of 70 on this exam with a SDof 20. Use the 68-95-99.7 rule to find the confidenceinterval of the true mean score of this placement exam.


B. Randomly selected cans of coke are measured for the amount ofcola in ounces. The 64 sample values obtained have a mean of 12.2ounces. The SD of the population is assumed to be 0.8 ounces. Icalculate a confidence interval and determined the upper limit tobe 12.5 and the lower limit to be 11.9. Use the 68-95-99.7(Emperical rule).
        1. is my level ofconfidence closer to 95% or 99%
        2. If I redo mycalculations using a sample of 100, will my confidence interval(for either 95% or    
          99%) bewider than or more narrow than that for a sample of 64?

Explanation / Answer

68% of the stuff will be within +-1 standard deviation 95% of the stuff will be within +-2 standard deviation 99.7% of the stuff will be within +-3 standard deviation

A. A writing placement exam is given to test takers across the U.S.A sample of 100 test takers has a mean of 70 on this exam with a SDof 20. Use the 68-95-99.7 rule to find the confidenceinterval of the true mean score of this placement exam.
so 20/sqrt(100)=2 sd of sample
68% of the scores will be within +-2 so (68,72) 95% of the scores will be within +-4 (66,74) 99.7% of the scores will be within +-6 (64,76)
68% of the scores will be within +-2 so (68,72) 95% of the scores will be within +-4 (66,74) 99.7% of the scores will be within +-6 (64,76) B. Randomly selected cans of coke are measured for the amount ofcola in ounces. The 64 sample values obtained have a mean of 12.2ounces. The SD of the population is assumed to be 0.8 ounces. Icalculate a confidence interval and determined the upper limit tobe 12.5 and the lower limit to be 11.9. Use the 68-95-99.7(Emperical rule).
        1. is my level ofconfidence closer to 95% or 99% .8/sqrt(64)=.1 SD 95% of the cans will be within +-.2 of 12.2 mean (12,12.4) 99.7% of the cans will be within +-.3 12.2 mean (11.9,12.5) so its closer to 99%         2. If I redo mycalculations using a sample of 100, will my confidence interval(for either 95% or     
          99%) bewider than or more narrow than that for a sample of 64? 95% of the cans will be within +-.2 of 12.2 mean (12,12.4) 99.7% of the cans will be within +-.3 12.2 mean (11.9,12.5) so its closer to 99% .8/sqrt(100)=.08 SD so it will be narrower A. A writing placement exam is given to test takers across the U.S.A sample of 100 test takers has a mean of 70 on this exam with a SDof 20. Use the 68-95-99.7 rule to find the confidenceinterval of the true mean score of this placement exam.
so 20/sqrt(100)=2 sd of sample
68% of the scores will be within +-2 so (68,72) 95% of the scores will be within +-4 (66,74) 99.7% of the scores will be within +-6 (64,76)

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