a. H 0 : μ = 400, H (^) A : μ > 400
b. H 0 : μ ≥ 400, H (^) A : μ ≠ 400
c. H 0 : μ = 400, H (^) A : μ ≠ 400
d. H 0 : μ ≠ 400, H (^) A : μ < 400
e. H 0 : μ ≥ 400, H (^) A : μ < 400
Free-Response
You attend a large university with approximately 15,000 students. You want to construct a 90%
confidence interval estimate, within 5%, for the proportion of students who favor outlawing country
music. How large a sample do you need?
- The local farmers association in Cass County wants to estimate the mean number of bushels of corn
produced per acre in the county. A random sample of 13 1-acre plots produced the following results
(in number of bushels per acre): 98, 103, 95, 99, 92, 106, 101, 91, 99, 101, 97, 95, 98. Construct a
95% confidence interval for the mean number of bushels per acre in the entire county. The local
association has been advertising that the mean yield per acre is 100 bushels. Do you think it is
justified in this claim? - Two groups of 40 randomly selected students were selected to be part of a study on dropout rates.
Members of one group were enrolled in a counseling program designed to give them skills needed to
succeed in school, and the other group received no special counseling. Fifteen of the students who
received counseling dropped out of school, and 23 of the students who did not receive counseling
dropped out. Construct a 90% confidence interval for the true difference between the dropout rates of
the two groups. Interpret your answer in the context of the problem. - A hotel chain claims that the average stay for its business clients is 5 days. One hotel believes that
the true stay may actually be fewer than 5 days. A study conducted by the hotel of 100 randomly
selected clients yields a mean of 4.55 days with a standard deviation of 3.1 days. What is the
probability of getting a finding as extreme, or more extreme than 4.55, if the true mean is really 5
days? That is, what is the P -value of this finding? - One researcher wants to construct a 99% confidence interval as part of a study. A colleague says
such a high level isn’t necessary and that a 95% confidence level will suffice. In what ways will
these intervals differ? - A 95% confidence interval for the true difference between the mean ages of male and female
statistics teachers is constructed based on a sample of 95 males and 62 females. Consider each of the
following intervals that might have been constructed:
I. (−4.5, 3.2)
II. (2.1, 3.9)
III. (−5.2, –1.7)
For each of these intervals,
(a) Interpret the interval, and
(b) Describe the conclusion about the difference between the mean ages that might be drawn from
the interval. - A 99% confidence interval for a population mean is to be constructed. A sample of size 20 will be