Question

n 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 [a]% and [b]% 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

Answer 1

Explanation:

Given that in testing the reliability of DNA results used in crime labs, the new procedure matched DNA results to suspects 46 out of 50 times.

i.e population proportion = 46/50 = 0.92

For 99% success rate

Here p the proportion follows normal distribution with mean = 0.92 and

Std error =
`√(0.92*0.08/50) \\=0.038`

Margin of error for 99% = ±2.58*0.038 = ±0.099

Confidence interval lower bound = 0.92-0.099 = 0.8210

Upper bound = 0.92+0.0999 ~1

so Confidence interval - (0.821,1)

(p cannot exceed 1 so 1 is taken)

We are 99% sure the that this new DNA match procedure correctly identifies susspects between (0.821, 1)

since 99% confidence interval contians 1, there is evidence at the .01 level that this procedure will successfully match DNA results 99% of the time