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

Coastline Lake/Stream Mountains

Gender

Female 18 16 11

Male 16 25 14

Ho: Gender and preferred hiking area are independent.

Ha: 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-SquareMean 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: 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.

Decision: Assume α = 0.05 (α < p-value)

DO NOT REJECT Ho.

Conclusion: There is NOT sufficient evidence to conclude that gender and hiking preference are independent.