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

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.)

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Delilah 2 months 2021-10-14T19:10:51+00:00 1 Answer 0 views 0

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    2021-10-14T19:12:08+00:00

    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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45:7+7-4:2-5:5*4+35:2 =? ( )