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M2209_Lab_1_Solutions - Lab 1 Question 1 Turn to page 522...

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Lab 1 Question 1 Turn to page 522 of your text and read the story for question 6. (A space is provided for you to copy the question if you wish.) ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ________________________________________________________________ a. Answer part (a) from the text book. [i.e., explain what probability is being measured] If the true percentage of children who did not attain the grade level standard really is 15.9%, there is 0.023 probability that in a (random) sample of 8500 students we would see a percentage as low as 15.1%. b. (i) ADDITION TO PART b : Calculate a 95% confidence interval. p ˆ ± z* SE( ) = ± z* p ˆ p ˆ n q p ˆ ˆ 0.151 ± 1.960 8500 ) 849 . 0 )( 151 . 0 ( = 0.151 ± 1.96*0.004 = (0.147, 0.155) or 14.7 to 15.5% (ii) Answer part (b) from this question in the text book ANSWER: Although a p-value of 2.3% is small, giving good evidence that the new reading program is better, we are confident that there’s only been a decrease of at most 1.2% (i.e., from 15.9% down to 14.7%). That is not necessarily a large enough change to recommend adoption of the new program. The difference, at most 1.2%, is unlikely to be important (i.e. of practical significance).
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Question 2 A school board is considering introducing a new teaching method for math. They are
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