3. Suppose that I survey 500 randomly selected US voters about whether or not they think Donald Trump should have been impeached, and 276 of the 500 respondents say "yes, he should have." a. Test the hypothesis that greater than 50% of US voters believe that Trump should have been impeached with an alpha of .05. b. Calculate a 95% confidence interval for the share of US voters who believe that President Trump should have been impeached. HINT: Let x=1 if a respondent thinks he should have been impeached and 0 otherwise. Then the sample mean of this variable equals the fraction of respondents who think he should have been impeached (276/500). The sample standard deviation is

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3. Suppose that I survey 500 randomly selected US voters about whether or not they think Donald Trump should have been impeached, and 276 of the
500 respondents say "yes, he should have."
a. Test the hypothesis that greater than 50% of US voters believe that Trump should have been impeached with an alpha of .05.
b. Calculate a 95% confidence interval for the share of US voters who believe that President Trump should have been impeached.
HINT: Let x=1 if a respondent thinks he should have been impeached and 0 otherwise. Then the sample mean of this variable equals the fraction of
respondents who think he should have been impeached (276/500). The sample standard deviation is
|276(1 – x)² + 224(0 – x)²
499
(You can check this by creating a column with 276 l's and 224 0's in Excel or another spreadsheet and then using the standard deviation function in that
program.)
Transcribed Image Text:3. Suppose that I survey 500 randomly selected US voters about whether or not they think Donald Trump should have been impeached, and 276 of the 500 respondents say "yes, he should have." a. Test the hypothesis that greater than 50% of US voters believe that Trump should have been impeached with an alpha of .05. b. Calculate a 95% confidence interval for the share of US voters who believe that President Trump should have been impeached. HINT: Let x=1 if a respondent thinks he should have been impeached and 0 otherwise. Then the sample mean of this variable equals the fraction of respondents who think he should have been impeached (276/500). The sample standard deviation is |276(1 – x)² + 224(0 – x)² 499 (You can check this by creating a column with 276 l's and 224 0's in Excel or another spreadsheet and then using the standard deviation function in that program.)
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