Question

In a poll of registered voters​ nationwide, 43% of those polled blamed oil companies the most for the recent increase in gasoline prices. the margin of error at the​ 95% confidence level for this point estimate is​ 2.4%. construct a​ 95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices.

Answer 1

Explanation:

Given that in a poll of registered voters​ nationwide, 43% of those polled blamed oil companies the most for the recent increase in gasoline prices

The margin of error at the​ 95% confidence level for this point estimate is​ 2.4%.

Confidence interval lower bound = 43-2.4% = 41.6%

Confidence interval upper bound = 43+2.4% = 45.4%

Hence confidence interval = (41.6%, 45.4%)

The length of the interval = 2 times margin of error = 4.8%

The mid value = 43%

Answer 2

In this case,
Point estimate (p) = 43% = 0.43 of the population
Error at 95% confidence level (e)= 2.4% = 0.024 of the population

Now,
True population proportion = p+/- e = 0.43+/- 0.024 = (0.406,0.454)

That is, the true proportion of the population who blame oil companies lies between 0.406 and 0.454.