10.33 According to Remodeling magazine, the average cost to convert an existing
ID: 2960101 • Letter: 1
Question
10.33 According to Remodeling magazine, the average
cost to convert an existing room into a home office with
custom cabinetry and rewiring for electronic equipment is
$5976. Assuming a population standard deviation of
$1000 and the sample of home office conversion prices
charged for 40 recent jobs performed by builders in a
region of the United States, examine whether the mean
price for home office conversions for builders in this
region might be different from the average for the nation
as a whole. The underlying data are in file XR10033.
Identify and interpret the p-value for the test. Using the
0.025 level of significance, what conclusion will be
reached?
File XR10033:
price
7213
5259
5106
5559
5437
4755
4329
6199
6679
7885
7370
5776
7104
5584
6800
6294
6010
5382
7196
5811
6460
5385
6159
9359
6066
7504
6067
5773
6335
6361
7619
5041
6878
5786
5571
8540
6345
5854
6592
6957
Explanation / Answer
Given n=40, xbar= 6310, s=1020.804
The test hypothesis is
Ho:=5976
Ha: not equal to 5976
The test statistic is
Z=(xbar-)/(s/n)
=(6310-5976)/(1020.804/sqrt(40))
= 2.07
The p-value is 2*P(Z>2.07) = 0.038 (check standard normal table)
Given a=0.025, since p-value is larger than a=0.025, we do not reject Ho.
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