9.110 For taxpayers having an adjusted gross income of $1 million or more, the I
ID: 2960097 • Letter: 9
Question
9.110 For taxpayers having an adjusted gross income of$1 million or more, the Internal Revenue Service reports
that the average deduction for gifts to charity was
$144,700. Curious to see how his state compares, a legislator
surveys a simple random sample of 200 taxpayers
from his state who are in this gross income category, with
the data as shown in file XR09110. Using the data in this
file, construct and interpret the 90% confidence interval
for the mean charitable-gifts deduction for all of the
state’s taxpayers who are in the $1 million or more
adjusted gross income category. Is $144,700 within the
confidence interval? Given the answer to the preceding
question, comment on whether the state’s taxpayers who
are in this income group might not be typical of those in
the nation as a whole in terms of their tax-deductible
charitable contributions.
FILE XR09110:
186067
160817
73207
135224
143421
135879
244009
178037
104844
142294
122066
101399
176035
164173
122695
156586
137002
105752
169769
181707
135613
249099
141078
161214
97501
178540
184409
202575
154785
108298
158322
194662
153857
139770
164619
141433
Explanation / Answer
Mean contrib = x-bar = 150219.525 Standard deviation of the contrib = s = 37703.90815 SE(standard error) = s/sqrt n = 37703.91/sqrt 200 = 2666.07 90% confidence interval for the population contribution is found by (x-bar - 1.645 * SE, x-bar + 1.645 * SE) = (150219.5 - 1.645 * 2666.07, 150219.5 + 1.645 * 2666.07) = ($145833.81, $154605.19) $144700 in the 90% confidence interval. So state taxpayers in this income group might not be typical of those in the whole of the nation (in terms of their tax-deductible charitable contributions)
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