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Unformatted text preview: STAT 350 Solution 7 25. (a) Following the same format used for most confidence intervals, i.e., statistic (critical value) (standard error), an interval estimate for 1 2 is: 2 2 2 1 1 1 2 1 ) 1 ( ) 1 ( ) ( n p p n p p z p p . (b) The response rate for noincentive sample: p 1 = 75/110 = .6818, while the return rate for the incentive sample is p 2 = 66/98 = .6735. Using z = 1.96 (for a confidence level of 95%), a twosided confidence interval for the true (i.e., population) difference in response rates 1 2 is: (.6818  .6735) (1.96) 98 ) 6735 . 1 )( 6735 (. 110 ) 6818 . 1 ( 6818 . = .0083 .1273 =(.119, .1356). The fact that this interval contains 0 as a plausible value of 1 2 means that it is plausible that the two proportions are equal. Therefore, including incentives in the questionnaires does not appear to have a significant effect on the response rate. (c) Let i p ~ denote the sample proportion by adding 1 success and 1 failure to the i th sample. We calculate ) 2 /( ) 1 ( ~ n x p i , where x is the number of successes (or failures, whichever is desired) in the sample. Then: 67857 . ) 2 110 /( ) 1 75 ( ~ 1 p and . 67 . ) 2 98 /( ) 1 66 ( ~ 2 p Using the format of the equation given in part (a) above, we have the following 95% confidence interval: 2 ) ~ 1 ( ~ 2 ) ~ 1 ( ~ ) ~ ~ ( 2 2 2 1 1 1 2 1 n p p n p p z p p 2 98 ) 67 . 1 ( 67 . 2 110 ) 67857 . 1 ( 67857 . 96 . 1 ) 67 . 67857 (. 1264 . 00857 . 004158 . 96 . 1 ) 00857 (. ( .1178, .1350) This interval contains 0, including incentives in the questionnaire does not appear to have a significant effect on the response rate. This is the same conclusion as in part (b)....
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 Spring '08
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 Statistics, Standard Error

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