A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 555 randomly selected Americans surveyed, 437 were in favor of the initiative. Round answers to 4 decimal places where possible. a) With 90% confidence the proportion of all Americans who favor the new Green initiative is between ____ and ____. b) If many groups of 555 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About ____ percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about ____ percent will not contain the true population proportion.

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A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 555 randomly selected Americans surveyed, 437 were in favor of the initiative. Round answers to 4 decimal places where possible.  a)  With 90% confidence the proportion of all Americans who favor the new Green initiative is between ____ and ____.  b)  If many groups of 555 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group.  About ____ percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about ____ percent will not contain the true population proportion.

comentezq · Accepted Answer

Step 1  Consider,  Number of Americans surveyed (n)=555  Number of Americans that are in favor of the initiative (x)=437  (a)  The sample proportion is computed as:  Sample proportion (p^)=xn  =437555  =0.7874  Step 2  From standard normal table, the z-score at 90% confidence level is 1.645.  The 90% confidence interval is computed as:  CI=p^±zα/2×p^(1−p^)n  =0.7874±1.645×(0.7874)(1−0.7874)555  =0.7874±0.0286  =(0.7588,0.8160)  Therefore, the proportion of Americans that favor the new Green Initiative is between 0.7588 and 0.8160.  Step 3  (b)  The confidence interval provides the range in which the population proportion is likely to fall in. In this case, there is 90% probability that the proportion of Americans that favor the new Green initiative is between 0.7588 and 0.8160.  If many groups of 555 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of

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