Question

Kate Sanders, a researcher in the department of biology at IPFW University, studied the effect of agriculture contaminants on the fish population for streams in Northeastern Indiana (April 2012). Specially designed traps collected samples of fish at each of four stream locations. A research question was, "Did the differences in agricultural contaminants found at the four locations alter the proportion of the fish population by gender?" Observed frequencies were as follows:

Stream Location
Gender A B C D
Male 49 44 49 39
Female 41 46 36 44
a. Focusing on the proportion of male fish at each location, test the hypothesis that the population proportions are equal for all four locations. Use a 0.05 level of significance.
P-value = _____
b. Does it appear that the differences in agricultural contaminants found at the four locations altered the fish population by gender?

Answer 1

H0 : population proportion are equal

H1: population proportion are not equal

Pvalue = 0.4779

There is no difference

Explanation:

Given the data:

Stream Location

Gender A B C D ______ total

Male 49 44 49 39 ___ 181

Female 41 46 36 44 _ 167

Total_90_90_85_83_348

H0 : population proportion are equal

H1: population proportion are not equal

(181*90)/348 = ; (181*90)/348 ; (181*85)/348...

Expected value :

46.81_46.81 _ 44.21 _ 43.17

43.19_43.19 _ 40.79 _ 39.83

(Observed - expected)² ÷ expected

Chi-Squared Values:

0.1024 _ 0.1687 _ 0.5190 _ 0.4027

0.1110 _ 0.1828 _ 0.5625 _ 0.4364

Chisquare :

0.1024 + 0.1687 + 0.5190 + 0.4027 + 0.1110 + 0.1828 + 0.5625 + 0.4364

Chisquare = 2.4855

Using the Pvalue from Chisquare calculator :

Pvalue at 0.05, df = 3 is 0.4779

Reject Null if ;

Pvalue < α

0.4779 > 0.05

Hence we fail to reject the null and conclude that population proportion are equal