Question

A Gallup Poll in July 2015 found that 26% of the 675 coffee drinkers in the sample said they were addicted to coffee. Gallup announced, "For results based on the sample of 675 coffee drinkers, one can say with 95% confidence that the maximum margin of sampling error is ±5 percentage points." (a) Confidence intervals for a percent follow the form estimate ± margin of error Based on the information from Gallup, what is the 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee? (Enter your answers to the nearest percent.) lower bound ____________ upper bound_______________

Answer 1

Answer: lower bound = 21%

upper bound = 31%

Explanation:

Let
`\hat{p}` be the sample proportion.

As per given we have,

sample size : n=675

`\hat{p}=26\%`

The maximum margin of sampling error with 95% confidence : E=±5%

We know that confidence interval is given by :-

`\hat{p}-E\leq p\leq\hat{p}+E\\\\\Rightarrow\ 26\%-5\%\leq p\leq 26\%+5\%\\\\ 21\%\leq p\leq31\%`

The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee :-

lower bound = 21%

upper bound = 31%