Each of 126 individuals of a certain mammal species was plac

Each of 126 individuals of a certain mammal species was placed in an enclosure containing equal amounts of each of six different foods. The frequency with which the animals choose each of the food was.
Food items (i)-N,A,W,G,M,C
(fi)-13,26,31,14,28,14
a.)Test the hypothesis that there is no preference among the food items.

b.)A sample of hibernating bats consisted of 44 males and 54 females. Test the hypothesis that the hibernating population consists of equal number of males and females.

Solution

Set up null and alternate as

H0: There is no preference among the food items

Ha: There is preference among the food items.

Two tailed chi square test

Prepare contingency table.

AS no preference is null hypothesis Expected for each food will be equal.

p value =0.00684

As p < 0.05 reject null hypothesis at 5% significance.

There is no statistical evidence to support that there is no preference among the food items.

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b) H0: males = females

   Ha: males not equal to females

Observed            44             54            98

Expected            49             49            98

Chi square    0.5102         0.5102      1.0204

df = 1

p value = 0.3124

As p > 0.5, accept the hypothesis that the hibernating population consists of equal number of males and females at 5% significance level.