Question
In: Math
Researchers at Consumer Reports recently found that fish are often mislabeled in grocery stores and restaurants....
Researchers at Consumer Reports recently found that fish are often mislabeled in grocery stores and restaurants. They are interested to know, however, if the proportion of mislabeling varies by type of fish. They collected data on 400 packages of tuna and 300 packages of mahi mahi and found that 110 and 95 were mislabeled, respectively.
a. What are the point estimates for the proportion of tuna and mahi mahi that are mislabeled?
b. Provide a 95% confidence interval estimate of the difference between the proportion of tuna and mahi mahi that is mislabeled.
c. Based on your answer to (b), would you say the rate of mislabeling is different for tuna and mahi mahi? Explain your answer.
d. Now, let's say we want to test whether the proportion of tuna mislabeled is lower than the proportion of mislabeled mahi mahi. Assuming a 99% confidence level, work through your hypothesis testing procedure below.
Solutions
Expert Solution
olution :
Given that,
= x1 / n1 = 110 / 400 = 0.275
1-
= 1 - 0.275 = 0.725
= x2 / n2 = 95 / 300 = 0.3167
1 -
= 1 - 0.3167 = 0.6833
(a)
Point estimate = -0.04167
At 95% confidence level the z is ,
Z
/2
= Z 0.025 = 1.96
(b)
95% confidence interval for p1 - p2 is
,
(
-
) 
Z/2 *
[(1-
) / n1 +
(1 -
) / n2]
(0.275 - 0.3167)
1.96 *
[(0.275 * 0.725) / 400 + (0.3167 * 0.6833) / 300]
-0.110 < p1 - p2 < 0.027
(-0.110 , 0.027)
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