3. Public Option. A 2009 poll evaluating support for the health care public opti

Question

3. Public Option. A 2009 poll evaluating support for the health care public option plan indicates that 70% of 819 Democrats and 42% of 783 Independents support the public option. A 95% confidence interval for the difference between (pDemocrat – pIndependent), where p is the proportion of those who support the public option, is (0.23, 0.33). Based on this information, determine if the following statements are true or false, and explain your reasoning.

(a) We are 95% confident that 23% less to 33% more Democrats support the health care public option plan than Independents.

(b) The margin of error for the interval is 0.1.

(c) A 90% confidence interval for (pDemocrat – pIndependent) would be narrower.

(d) 95% of random samples of 819 Democrats and 783 Independents will yield differences in sample proportions between 23% and 33%.

(e) A 95% conf ence interval for (pIndependent – pDemocrat) is (–0.33, –0.23).

Explanation / Answer

(a) We are 95% confident that 23% less to 33% more Democrats support the health care public option plan than Independents. False ( it is from 23% to 33 % more Democrats will support  the health care public option plan than Independents.)

b) (b) False (As margin of error =(upper limit-lowwer limit)/2 =(0.33-0.23)/2

=0.05)

c)true ; as we decrease confidence interval ; critical z score will reduce and therefore width would be narrower

d)

true ; as above confidence interval is bsed on that size and that is correct interpretation of 95% CI

e) true ; as  (pIndependent – pDemocrat) =-(pDemocrat – pIndependent)

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