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How do the fares for airlines that directly compete compare?The accompanying table contains roundtrip fares for nonstop travel from a particular city to 10 different destinations in the same country on two airlines that a frequent flyer collected. The test is a two-tailed test. In the formula for the test statistic,D is the sample mean difference,up is the hypothesized mean difference,Sp is the standard deviation of the sample differences,and n is the number of matched pairs. At the 0.10 level of significance, What is the test​ statistic? Airline A Fare (S) 712 701 1004 1137 647 985 947 707 1152 1189 Airline B Fare(S) 715 704 1007 1140 650 988 950 710 1178 1192

Question

How do the fares for airlines that directly compete compare?The accompanying table contains roundtrip fares for nonstop travel from a particular city to 10 different destinations in the same country on two airlines that a frequent flyer collected. The test is a two-tailed test. In the formula for the test statistic,D is the sample mean difference,up is the hypothesized mean difference,Sp is the standard deviation of the sample differences,and n is the number of matched pairs. At the 0.10 level of significance, What is the test​ statistic? Airline A Fare (S) 712 701 1004 1137 647 985 947 707 1152 1189 Airline B Fare(S) 715 704 1007 1140 650 988 950 710 1178 1192

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Solution

To calculate the test statistic, we first need to calculate the sample mean difference (D), the standard deviation of the sample differences (Sp), and the number of matched pairs (n).

  1. Calculate the differences between the fares of Airline A and Airline B for each destination.

  2. Calculate the mean of these differences (D).

  3. Calculate the standard deviation of these differences (Sp).

  4. The number of matched pairs (n) is the number of destinations, which is 10.

  5. The hypothesized mean difference (up) is typically 0 in a two-tailed test, unless otherwise specified.

The formula for the test statistic is (D - up) / (Sp / sqrt(n)).

Plug in the values you calculated for D, Sp, and n into this formula to get the test statistic.

Note: The actual calculations for D, Sp, and the test statistic depend on the specific differences between the fares of Airline A and Airline B for each destination.

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