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Published byJanis Bailey Modified over 8 years ago

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The table shows a random sample of 100 hikers and the area of hiking preferred. Are hiking area preference and gender independent? Hiking Preference Area CoastlineLake/StreamMountains Gender Female 181611 Male 162514

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H o : Gender and preferred hiking area are independent. H a : Gender and preferred hiking area are not independent.

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The table contains the observed (O) frequencies. If the null hypothesis is true, the expected percentages (E) are calculated by the formula (row total)(column total) ÷ total surveyed A Test of Independence is right-tailed. The degrees of freedom (df) = (# rows – 1)(# columns – 1) = (2 – 1)(3 – 1) = 2

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Distribution for the Test: Chi-Square Mean of the distribution = number of dfs = 2 To find the pvalue: Go to MATRIX in calculator, scroll to EDIT, choose [A] We have a 2 x 3 matrix. Enter the values from the table into the matrix. QUIT. Go to STAT, TESTS, scroll down to χ2-test, press Enter. Press Enter, Enter, Enter. The test statistic and p-value are given.

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Test statistic: 1.4679 p-value: 0.4800 If the Null is true, there is a 0.4800 probability that the test statistic is greater than 1.4679.

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Decision: Assume α = 0.05 (α < p-value) DO NOT REJECT H o. Conclusion: There is NOT sufficient evidence to conclude that gender and hiking preference are independent.

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