Question

A random sample of 870 people was taken from those who were selected to serve on a grand jury in Hidalgo County, Texas over an 11-year period of time. Out of the sample, 348 of them were Mexican-Americans. a. Use this sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were Mexican-Americans. Make sure to show all components necessary to construct the confidence interval. Round your final answer to 3 decimal places. b. Of all the people eligible for jury duty, 79.1% of them were Mexican-Americans. Does it seem like there was discrimination in the jury selection process? Justify your answer.

Answer 1

348 870 - 0.4. (proportion of people who were Merican American) Pci-p) + Zab. Ŝ - Zapin 94.4 C.I of proportion | P(1-2) p < [24 n Z 2-576 0-005 source- STATKEY Cimape attacked) = 0.4 2.576x 0.4x0.6 870 <p < 0.4 + 2-576x/6.4x0.6 870 0.443 0.443) 0.357 < p < (0.357 , 991 9 @ According to the above confidence interval, we are confident that the true proportion of Mexican American ties in the interval (35.7% , 44.37) the people eligible for Jury clata , 79.16 here Mexican-Americans . As 791% does not lie in the interval above confidence 9 we can conclude that there was diserinuination in the Jury selection process Nowg aming

StatKey Theoretical Distribution Normal Distribution- Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean Standard Deviation 0.40 0 1 0.35 Edit Parameters 0.30 0.25 0.20 0.0050 0.990 0.0050 0.15 0.10 0.05 0.00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 -2.576 2.576 Activate Windows

The 99% C.I is obtained using the formula mentioned. The critical value is obtained from STATKEY (image attached for reference). As 79.1% does not lie in the obtained confidence interval, there has been a discrimination in the jury selection process.