An airline transports over 10,000 passengers daily, and the airline is curious what proportion of their passengers use mobile boarding passes instead of paper passes. They take an SRS of 80 passengers and find that 60 of them use mobile boarding passes.

Based on this sample, which of the following is a $95 \%$ confidence interval for the proportion of passengers who use mobile boarding passes?

Choose 1 answer:
(A) $(0.625,0.875)$
(B) $(0.637,0.863)$
(C) $(0.655,0.845)$
(D) $(0.670,0.830)$

Question

An airline transports over 10,000 passengers daily, and the airline is curious what proportion of their passengers use mobile boarding passes instead of paper passes. They take an SRS of 80 passengers and find that 60 of them use mobile boarding passes.

Based on this sample, which of the following is a $95 \%$ confidence interval for the proportion of passengers who use mobile boarding passes?

Choose 1 answer:
(A) $(0.625,0.875)$
(B) $(0.637,0.863)$
(C) $(0.655,0.845)$
(D) $(0.670,0.830)$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the 95% confidence interval for the proportion of passengers using mobile boarding passes, we start with the sample proportion (p^^) which is 60/80 or 3/4. ‖ ‖ step 2 ⋮ Using the asksia-ll calculator result, the 95% confidence interval is calculated as 0.6551 to 0.8449. ‖ ‖ step 3 ⋮ This interval is obtained using the formula for the standard confidence interval for a binomial parameter: p^^ ± sqrt(((1 - p^^) p^^)/n) z_((1 - c)/2), where p^^ is the sample proportion, n is the sample size, and c is the confidence level. ‖ ‖ step 4 ⋮ The z-score corresponding to a 95% confidence level is not explicitly given, but it is typically around 1.96 for a two-tailed test. This value is used in the calculation of the confidence interval. ‖ ∻[1] Answer∻ ***C*** ∻Key Concept∻ ⚹Binomial Proportion Confidence Interval⚹ ∻Explanation∻ ⚹The confidence interval for a proportion is calculated using the sample proportion, sample size, and the z-score corresponding to the desired confidence level. It provides a range within which the true population proportion is likely to fall with a certain level of confidence.⚹◊What is the formula for calculating the margin of error in a confidence interval for sample proportions?⍭ Generate me a similar question◊

Sia