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.

gender	A	B	C	D
male	53	48	53	43
female	37	42	32	40

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.

(a.) H₀: Not all population proportions are equal.
H_a: p_A = p_B = p_C = p_D

_(b.)  H₀: All population proportions are not equal.
H_a: p_A = p_B = p_C = p_D

_(c.) H₀: p_A = p_B = p_C = p_D
H_a: Not all population proportions are equal.

(d.)  H₀: p_A = p_B = p_C = p_D
H_a: All population proportions are not equal.

A-1.) Find the value of the test statistic. (Round your answer to three decimal places.) =___________________

A-2.) What is the p-value? (Round your answer to four decimal places.)

p-value =____________

A-3)What is your conclusion?

(a.) Reject H₀. We cannot reject the hypothesis that the population proportions are equal in each location.

(b.) Do not reject H₀. We cannot reject the hypothesis that the population proportions are equal in each location.    

(c.) Do not reject H₀. We conclude that the population proportions are not equal in each location.

(d.) Reject H₀. We conclude that the population proportions are not equal in each location.

B) Does it appear that differences in agricultural contaminants found at the four locations altered the fish population by gender?

(a.) Yes, there is evidence that differences in agricultural contaminants found at the four locations altered the fish population by gender.

(b.) No, there is no evidence that differences in agricultural contaminants found at the four locations altered the fish population by gender.    

Answer 1

A]

State the null and alternative hypotheses.

Null hypothesis: All population proportions are equal that is $H_0:$$p_A = p_B = p_C = p_D$

Alternative hypothesis: $H_a:$ Not all population proportions are equal

Option C] is correct choice

A-1]

The value of the test statistic F = 0.070

A-2]

The p-value = 0.9740

A-3]

Conclusion :

Here P-value is greater than level of significant 0.05

Do not reject H₀. We cannot reject the hypothesis that the population proportions are equal in each location.

Option b] is correct choice

B) Does it appear that differences in agricultural contaminants found at the four locations altered the fish population by gender?

(b.) No, there is no evidence that differences in agricultural contaminants found at the four locations altered the fish population by gender.