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 differ- ences in sample proportions between 23% and 33%.

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

Explanation / Answer

Here we have given that 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.

That is,

p1^ = 42% = 0.42

p2^ = 95% = 0.95

n1 = 819

n2 = 783

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).

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

This is false statement.

The correct statement is we are 95% confident that the population mean difference lies between 0.23 and 0.33

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

This is also false statement.

p^ - E = 0.23

p^ + E = 0.33

By adding these two equations we get E = 0.05

c) The correct statement will be the margin of error will be 0.05

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

This will be correct statement.

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

This is also correct statement.

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