Question

Recent incidents of food contamination have caused great concern among consumers. An article reported that 31 of 80 randomly selected Brand A brand chickens tested positively for either campylobacter or salmonella (or both), the leading bacterial causes of food-borne disease, whereas 64 of 80 Brand B brand chickens tested positive.

(a)

Does it appear that the true proportion of non-contaminated Brand A chickens differs from that for Brand B? Carry out a test of hypotheses using a significance level 0.01. (Use p₁ for Brand A and p₂ for Brand B.)

State the relevant hypotheses.

H₀: p₁ − p₂ = 0
H_a: μ₁ − μ₂ > 0H₀: p₁ − p₂ = 0
H_a: p₁ − p₂ < 0    H₀: p₁ − p₂ > 0
H_a: p₁ − p₂ = 0H₀: p₁ − p₂ < 0
H_a: p₁ − p₂ = 0H₀: p₁ − p₂ = 0
H_a: p₁ − p₂ ≠ 0

Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z=P-value=

State the conclusion in the problem context.

Reject H₀. The data does not suggest the true proportion of non-contaminated chickens differs for the two companies.Reject H₀. The data suggests that the true proportion of non-contaminated chickens differs for the two companies.    Fail to reject H₀. The data suggests the true proportion of non-contaminated chickens differs for the two companies.Fail to reject H₀. The data does not suggest that the true proportion of non-contaminated chickens differs for the two companies.

(b)

If the true proportions of non-contaminated chickens for the Brand A and Brand B are 0.50 and 0.25, respectively, how likely is it that the null hypothesis of equal proportions will be rejected when a 0.01 significance level is used and the sample sizes are both 100? (Round your answer to four decimal places.)

Answer 1

Let, p1 is the true proportion of non-contaminated Brand A

And p2 is the true proportion of non-contaminated Brand B