Question

1) Recent incidents of food contamination have caused great concern among consumers. An article reported that 36 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 68 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 Ha: μ1 − μ2 > 0 H0: p1 − p2 > 0 Ha: p1 − p2 = 0 H0: p1 − p2 = 0 Ha: p1 − p2 ≠ 0 H0: p1 − p2 < 0 Ha: p1 − p2 = 0 H0: p1 − p2 = 0 Ha: p1 − p2 < 0 Correct: Your answer is correct. 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=

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. Fail to reject H0. The data suggests 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 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.)

2)Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data were obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the significant changes were as follows.

Before:	12	28	68	122	65	63
After:	13	26	45	84	76	72

(a) The article included the statement "A paired t-test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs." Carry out such a test. [Note: The relevant normal probability plot shows a substantially linear pattern.]
State and test the appropriate hypotheses. (Use

α = 0.05.)

H₀: μ_D = 0
H_a: μ_D ≥ 0H₀: μ_D = 0
H_a: μ_D ≠ 0    H₀: μ_D = 0
H_a: μ_D ≤ 0H₀: μ_D = 0
H_a: μ_D < 0H₀: μ_D = 0

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

t	=
P-value	=

State the conclusion in the problem context.

Reject H₀. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs. Reject H₀. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.    Fail to reject H₀. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs. Fail to reject H₀. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.

(b) If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in a number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)

Answer 1