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Karo-lina-s [1.5K]
3 years ago
10

A Gallup Poll in July 2015 found that 26% of the 675 coffee drinkers in the sample said they were addicted to coffee. Gallup ann

ounced, "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.)
Mathematics
1 answer:
emmasim [6.3K]3 years ago
4 0

Answer:

The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee is between 21% and 31%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

A confidence interval has two bounds, the lower and the upper

Lower bound:

\pi - M

Upper bound:

\pi + M

In this problem, we have that:

\pi = 0.26, M = 0.05

Lower bound:

\pi - M = 0.26 - 0.05 = 0.21

Upper bound:

\pi + M = 0.26 + 0.05 = 0.31

The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee is between 21% and 31%.

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