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An airline is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto their Long Beach (LGB) to San Francisco (SFO) flights. Since Option 1 has more automation, the airline suspects that the mean Option 1 loading time is less than the mean Option 2 loading time. To see if this is true, the airline selects a random sample of 285 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.7 minutes, with a sample standard deviation of 5.7 minutes. They also select an independent random sample of 205 flights from LGB to SFO using Option 2 and record their loading times. The sample mean is found to be 18.3 minutes, with a sample standard deviation of 4.1 minutes. Since the sample sizes are quite large, it is assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimated to be the sample standard deviation values given above. At the 0.05 level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, u, , is less than the mean Option 2 loading time, µ, for the airline's flights from LGB to SFO? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)

An airline is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto their Long Beach (LGB) to San Francisco (SFO) flights. Since Option 1 has more automation, the airline suspects that the mean Option 1 loading time is less than the mean Option 2 loading time. To see if this is true, the airline selects a random sample of 285 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.7 minutes, with a sample standard deviation of 5.7 minutes. They also select an independent random sample of 205 flights from LGB to SFO using Option 2 and record their loading times. The sample mean is found to be 18.3 minutes, with a sample standard deviation of 4.1 minutes. Since the sample sizes are quite large, it is assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimated to be the sample standard deviation values given above. At the 0.05 level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, u, , is less than the mean Option 2 loading time, µ, for the airline's flights from LGB to SFO? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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An airline is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto their Long Beach (LGB) to San Francisco (SFO) flights. Since Option 1 has more automation, the airline suspects that the mean Option 1 loading time is less than the mean Option 2 loading time. To see if this is true, the airline selects a random sample of 285 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.7 minutes, with a sample standard deviation of 5.7 minutes. They also select an independent random sample of 205 flights from LGB to SFO using Option 2 and record their loading times. The sample mean is found to be 18.3 minutes, with a sample standard deviation of 4.1 minutes. Since the sample sizes are quite large, it is assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimated to be the sample standard deviation values given above. At the 0.05 level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, u, , is less than the mean Option 2 loading time, u, for the airline's flights from LGB to SFO? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
Transcribed Image Text:An airline is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto their Long Beach (LGB) to San Francisco (SFO) flights. Since Option 1 has more automation, the airline suspects that the mean Option 1 loading time is less than the mean Option 2 loading time. To see if this is true, the airline selects a random sample of 285 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.7 minutes, with a sample standard deviation of 5.7 minutes. They also select an independent random sample of 205 flights from LGB to SFO using Option 2 and record their loading times. The sample mean is found to be 18.3 minutes, with a sample standard deviation of 4.1 minutes. Since the sample sizes are quite large, it is assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimated to be the sample standard deviation values given above. At the 0.05 level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, u, , is less than the mean Option 2 loading time, u, for the airline's flights from LGB to SFO? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H and the alternative hypothesis H,. H, : 미 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) (e) Can we support the claim that the mean Option 1 loading time is less than the mean Option 2 loading time for the airline's flights from LGB to SFO? O Yes O No olo
Transcribed Image Text:(a) State the null hypothesis H and the alternative hypothesis H,. H, : 미 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) (e) Can we support the claim that the mean Option 1 loading time is less than the mean Option 2 loading time for the airline's flights from LGB to SFO? O Yes O No olo
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