Question

Kate Sanders, a researcher in the department of biology at PFW University, studied the effect of agricultural contaminants on the stream fish population 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

Answer 1

Full question attached

Answer and explanation:

Null hypothesis : all population proportions are equal, p1=p2=p3=p4

Alternative hypothesis : Not all population proportions are equal

To find our p-value using chi Square method, we first find expected frequencies from observed frequencies above

Expected Frequencies:

Gender A. B. C. D

Male. 46.81 46.81 44.21 43.17

Female 43.19. 43.19 40.79 39.83

Total = 348

chi Square for table = (observed frequency - expected frequency)²/expected frequency

Gender. A. B. C. D

Male. 0.10 0.17 0.52 0.40

Female 0.11 0.18 0.56 0.44

x²= 2.49

Degrees of freedom(df)= k – 1 = (4 – 1) = 3

Using the chi Square table with degree of freedom = 3, 2 and x²= 2.49 shows, the p –value = 0.4771 therefore we do not reject null hypothesis since p value is greater than significance level 0.08

We do not reject the null hypothesis

b. There is no evidence of differences in proportion