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

Test statistic: Measures how far the observed values are from the expected values. p-value:

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

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