Question

You may need to use the appropriate technology to answer this question A researcher in a university's biology department studied the effect of agriculture contaminants on the stream fish population in northeastern Indiana. 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?" Suppose observed frequencies were as follows Stream Locations Gender ABIC D Male49 44 49 39 Female 41 4636 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 State the null and alternative hypotheses Ha: Not all population proportions are equal Ha: All population proportions are not equal H: All population proportions are not equal 0 Ho: Not all population proportions are equal Find the value of the test statistic. (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value What is your conclusion? Do not reject H We cannot reject the hypothesis that the population proportions are equal in each location O Reject Ho. We cannot reject the hypothesis that the population proportions are equal in each location Do not reject Ho We conclude that the population proportions are not equal in each location Reject Ho. We conclude that the population proportions are not equal in each location 0 (b) Does it appear that differences in agricultural contaminants found at the four locations altered the fish population by gender? O Yes, there is evidence that differences in agricultural contaminants found at the four locations altered the fish population by gender No, there is no evidence that differences in agricultural contaminants found at the four locations altered the fish population by gender

Answer 1

We will use chi-square test for this problem.

a)

• Null and Alternative hypothesis

H_o : p_A = p_B = p_C = p_D

H_a : All population proportions are not equal.

Observed Frequencies (f_ij) are:

Gender	Stream Locations
	A	B	C	D	Total
Male	49	44	49	39	181
Female	41	46	36	44	167
Total	90	90	85	83	348

Expected frequencies are calculated for each cell in a contingency table by the formula :

$\dpi{100} \fn_cm E_{ij} =\frac{T_{i}\times T'_{j} }{N}$

• E_ij = expected frequency for the i^th row and j^th column
• T_i = total in the i^th row
• T'_j = total in the j^th column
• N = table grand total

Expected frequencies (e_ij) are :

Gender	Stream Locations
	A	B	C	D	Total
Male	46.81	46.81	44.21	43.17	181
Female	43.19	43.19	40.79	39.83	167
Total	90	90	85	83	348

Chi Square Statistics is given by :

$\fn_cm \chi ^{2} = \sum \frac{\left ( f_{ij} - e_{ij}\right )^{2}}{e_{ij}}$

Chi Square calculations are :

Gender	Stream Locations
	A	B	C	D	Total
Male	0.10	0.17	0.52	0.40	1.19
Female	0.11	0.18	0.56	0.44	1.29
					$\fn_cm \chi ^{2}$= 2.49

Value of test statistics = 2.49

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

Using the $\fn_cm \chi ^{2}$ table, for  df = 3, $\fn_cm \chi ^{2}$ = 2.49  the p–value is = 0..4771

p-value > 0 .05, so we

Do not reject H₀. We cannot reject the hypothesis that the population

proportion are equal in each locations.

b)  No, There is no evidence that differences in agricultural contaminants found at the four  locations have

altered the gender proportions of the fish populations.