For good or bad, statistical evidence is very important in this country for civi
ID: 3321248 • Letter: F
Question
For good or bad, statistical evidence is very important in this country for civil rights and discrimination cases. The supreme court has made important rulings which effect all subsequent trials in lover courts. In castaneda Vs. partida the court noted that 79% of the population of Hidalgo county had spanish sounding last names. Of the 870 juror selected to jury panels by the county only 339 had spanish sounding last names.
a) Let p be the true population of jurors which spanish speaking surnames. If the juries are truly selected at random, without regard to ethnicity, what should p^ be?
b) Let p^ be the proportion of jurors with spanish sounding last names in a sample of 870. Assuming the jurors are selected or random, what is probability of the sample proportion being less than or equal to 0.39? How many standard deviation is our observed proportion of p^=0.39 from the assumed proportion, p?
c) Give a 95% confidence interval for p the true proportion of jurors with spanish sounding last names.
d) Thinking of this problems as hypothesis test, state the null and alternative hypotheses being used by the lawyer representing the minority citizens of Hidalgo County both with mathematical symbols and in English
e) Based on your calculations from part b and c would you be inclined to fail to reject or reject the null hypothesis? Do you suspect discrimination? Why or why not? Briefly explain.
Explanation / Answer
a) Let p be the true population of jurors which spanish speaking surnames. If the juries are truly selected at random, without regard to ethnicity, what should p^ be?
Answer : If the juries are truly selected at random, without regard to ethnicity,
p^ = 0.79
(b) Let p^ be the proportion of jurors with spanish sounding last names in a sample of 870. Assuming the jurors are selected or random, what is probability of the sample proportion being less than or equal to 0.39? How many standard deviation is our observed proportion of p^=0.39 from the assumed proportion, p?
Answer : Here,
standard error of proportion se0 = sqrt [0.79 * 0.21/870] = 0.0138
Pr(p^ < 0.39) =Pr(p^ =< 0.39 ; 0.79; 0.0138)
Z = (0.39 - 0.79)/ 0.0138 = -29.00
It is 29 standard deviation aways from from the assumed proportion, p
c) Give a 95% confidence interval for p the true proportion of jurors with spanish sounding last names.?
95% confidence interval = p^ +- Z95% sqrt [p^ * (1-p^/ N]
= 0.39 +- 1.96 * sqrt [0.39 * 0.61/870]
= 0.39 +- 0.0324
= (0.3576, 0.4224)
d) Thinking of this problems as hypothesis test, state the null and alternative hypotheses being used by the lawyer representing the minority citizens of Hidalgo County both with mathematical symbols and in English
Answer : Null hypothesis : H0 : The proportions jurors from minority community is same as the proportion of minority community population in Hindalgo country. p = p0
Alternative Hypothesis : Ha : The proportions jurors from minority community is less than e proportion of minority community population in Hindalgo country. p < p0
e) Based on your calculations from part b and c would you be inclined to fail to reject or reject the null hypothesis? Do you suspect discrimination? Why or why not? Briefly explain.
We we reject the null hypothesis and can conclude that there is some discrimination with minority community.
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