The following are airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport. 269 255 267 285 274 275 266 258 271 281
(a) Compute a 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles. (Round your answers to three decimal places.)
(b) Give an interpretation of the 90% confidence level associated with the interval estimate in part (a).
a) If we were to take a large number of random samples of size 10, 10% of the resulting confidence intervals would contain the true mean airborne time.
b) If we were to take a large number of random samples of size 90, 10% of the resulting confidence intervals would contain the true mean airborne time.
c)If we were to take a 10 random samples of size 10, 10% of the resulting confidence intervals would contain the true mean airborne time.
d) If we were to take a large number of random samples of size 10, 90% of the resulting confidence intervals would contain the true mean airborne time.

Question

24-11-2022
Mathematics

contestada

The following are airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport. 269 255 267 285 274 275 266 258 271 281
(a) Compute a 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles. (Round your answers to three decimal places.)
(b) Give an interpretation of the 90% confidence level associated with the interval estimate in part (a).
a) If we were to take a large number of random samples of size 10, 10% of the resulting confidence intervals would contain the true mean airborne time.
b) If we were to take a large number of random samples of size 90, 10% of the resulting confidence intervals would contain the true mean airborne time.
c)If we were to take a 10 random samples of size 10, 10% of the resulting confidence intervals would contain the true mean airborne time.
d) If we were to take a large number of random samples of size 10, 90% of the resulting confidence intervals would contain the true mean airborne time.

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NGireesh NGireesh · Answer 1 · 2022-11-26T09:28:58+01:00

90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles is (264.639, 275.5066), if 10 randomly selected flights from San Francisco to Washington Dulles airport.

Define confidence interval.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.

Given,

Airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport.

269 255 267 285 274 275 266 258 271 281

Sample mean = 270.10

Standard deviation = 9.326

Sample size = 10

Confidence level = 90%

Formula:

Confidence interval

= x ± tₐ₎₂(s/√n)

= 270 ± 1.833(9.326/√10)

= 270.1 ± 5.4066

= (264.639, 275.5066)

90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles is (264.639, 275.5066), if 10 randomly selected flights from San Francisco to Washington Dulles airport.

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