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.

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Presentation transcript:

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 Male

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

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

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.

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

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.