Question

The following are airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport.

269 257 268 284 274 275 266 258 271 281

(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.) ,

Answer 1

Solution:

The 90% confidence interval for population mean is given as follows:

(a + cupon-1)

Where, x̄ is sample mean, s is sample standard deviation, n is sample size and t_{(0.10/2, n-1)} is critical t-value to construct 90% confidence interval.

-CN

- - Σίσι - 33

We have, n = 10

C = (269 + 257 + .…………. + 281) = = = 270.3 10

s = VI. |(269 – 270.3)2 + ........... + (281 – 270.3)2

s = 76.9 = 8.7693

Using t-table we get, t_{(0.10/2, 10-1)} = 1.833

Hence, 90% confidence interval is,

270.3 +1.833 x 8.7693 10

=(270.3±5.083)

=(270.3-5.083, 270.3+5.083)

= (265.217,275.383)

Hence, 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles is,

(265.217 minutes, 275.383 minutes)

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