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 time Obviously for the purpose of convincing Junes 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 suspects between and p6 of the time Using the same sample, is there evidence at the 01 level that this procedure will successfully match DNA results 90% of the time Ho p | 99% ??: 99% State your conclusion: There procedure will match DNA results 99% of the time (isis not) statistically significant evidence at the 01 level that this new

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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