Question 1
Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labeled A and B) and recorded the prices charged by each supermarket. The summary results are provided below:
A = 2.09
B = 1.99
= .10
sA = 0.22
sB = 0.19
sd = .03
Assuming the data represent a matched pairs design, calculate the confidence interval for comparing mean prices using a 95% confidence level.
◦ .10 ± .004935
◦ .10 ± .1255
◦ .10 ± .00588
◦ .10 ± .056975
Question 2
A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Suppose the following 95% confidence interval for
μA -
μB was calculated: (100, 2500). Which of the following inferences is correct?
◦ We are 95% confident that no significant differences exists in the mean number of hours of continuous use before breakdown of engines using oils A and B.
◦ We are 95% confident that an engine using oil B has a higher mean number of hours of continuous use before breakdown than does an engine using oil A.
◦ We are 95% confident that an engine using oil A has a higher mean number of hours of continuous use before breakdown than does an engine using oil B.
◦ We are 95% confident that the mean number of hours of continuous use of an engine using oil A is between 100 and 2500 hours.
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