a) Do these data support the community’s claim at a 1% level of significance? (b) What is the significance level of the data (a value)? (c) How do we interpret the 1% significance level in this context? Be very specific.
*PART (A) is the hypothesis tests through all steps, including the
English conclusion. The parts that follow may seem redundant, but I want
separate (and labelled) answers for them, anyway. Finally, I want no
reference to “hypothesis” in any final answers
1. A fire insurance company felt that the mean distance from a home to the
nearest fire department in a suburb of Boston was at least 4.7 miles. It set its
fire insurance rates accordingly. Members of the community set out to show
that the mean distance was, in fact, less than 4.7 miles in order to convince
the insurance company to lower its rates, so a random sample of 61 homes
was selected and the distance to the nearest fire department recorded. The
mean distance was found to be 4.4 miles with standard deviation 2.4 miles.
(a) Do these data support the community’s claim at a 1% level of
significance?
(b) What is the significance level of the data (a value)?
(c) How do we interpret the 1% significance level in this context? Be
very specific.
2. A study involving two groups of women from six large city hospitals was
conducted to determine the relationship, if any, of caffeine consumption
between pregnant women and infertile women (defined as not conceiving
after one year of unprotected intercourse). The women were asked about
their daily intake of regular or decaffeinated coffee and tea, as well as
weekly consumption of cola. The 2,817 pregnant women had a mean
daily caffeine intake of 520.5 mg with standard deviation 120.5 mg.
The 1,818 infertile women had a mean daily caffeine intake of 535.2 mg
with standard deviation 176.3 mg.
(a) At a 5% significance level, do the data indicate a significant difference
in caffeine consumption between pregnant and infertile women.
(b) Are your results significant? Why or why not?
(c) Give one interpretation for the p-value in this context.
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