In testing the reliability of DNA results used in crime labs, the new procedure

Question

In testing the reliability of DNA results used in crime labs, the new procedure matched DNA results to suspects 46 out of 50 times. Obviously for the purpose of convincing juries the labs like to how a 99% success rate. State a +4 99% confidence interval for the proportion of results that are matched successfully: We are 99% sure the that this new DNA match procedure correctly identifies susspects between % and % of the time. Using the same sample, is there evidence at the .01 level that this procedure will successfully match DNA results 99% of the time? Ho: p 9996 Ha: p 99% State your conclusion: There match DNA results 99% of the time. (is/is not) statistically significant evidence at the.01 level that this new procedure will

Explanation / Answer

n = 50

p = 0.92

z-value of 99% CI = 2.5780

SE = sqrt(p*(1-p)/n) = 0.03837

ME = z*SE = 0.09891

Lower Limit = p - ME = 0.82109

Upper Limit = p + ME = 1.01891

90% CI (0.8211 , 1.0189 )

we are 99% confident that this new DNA match procedure correctly identifies suspects between (0.8211) 82.11% and 101.89%

H0 : p = 99%

Ha : p not equal to 99%

z = (P - p) / sqrt(p * (1 -p)/n))

= (0.92 - 0.99) / sqrt(0.99 * 0.01 /50)

= -4.9747

P value = 0.00001

There is statistically significant evidence at the 0.01 level

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