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Mathematics

Can you do chapter 8?

8.
a.
Since n is small, an assumption that the population is at least approximately normal is required so
that the sampling distribution of x can be approximated by a normal distribution.
b.
Margin of error:
z.025 ( / n ) = 1.96(5.5 / 10) = 3.41
c.
Margin of error:
z.005 ( / n ) = 2.576(5.5 / 10) = 4.48
12. a.
2.179
b.
-1.676
c.
2.457
d.
Use .05 column, -1.708 and 1.708
e.
Use .025 column, -2.014 and 2.014
x t / 2 (s / n )
15.
90% confidence
df = 64
t.05 = 1.669
19.5 ± 1.669 (5.2 / 65)
19.5 ± 1.08 or 18.42 to 20.58
95% confidence
df = 64
19.5 ± 1.998 (5.2 / 65) 19.
t.025 = 2.015
t.025 = 1.998
a.
t.025 (s / n )
df = 44
s = 65
2.015 (65 / 45) = 19.52 or approximately $20
b.
x t.025 (s / n )
273 ± 20 or 253 to 293
c.
At 95% confidence, the population mean is between $253 and $293. This is definitely above the
$229 level of 2 years ago. Hotel room rates are increasing.
The point estimate of the increase is $273 - $229 = $44 or 19%.
19.5 ± 1.29 or 18.21 to 20.79
19. a.
t.025 (s / n )
df = 44
t.025 = 2.015
s = 65
2.015 (65 / 45) = 19.52 or approximately $20
b.
x t.025 (s / n )
273 ± 20 or 253 to 293
c.
At 95% confidence, the population mean is between $253 and $293. This is definitely above the
$229 level of 2 years ago. Hotel room rates are increasing.
The point estimate of the increase is $273 - $229 = $44 or 19%.
26. a.
n=
2
z.025
2 (1.96) 2 (.25) 2
=
= 24.01 Use 25.
E2
(.10) 2
If the normality assumption for the population appears questionable, this should be adjusted upward
to at least 30.
b.
c.
(1.96) 2 (.25) 2
= 49 Use 49 to guarantee a margin of error no greater than .07. However, the US
(.07) 2
EIA may choose to increase the sample size to a round number of 50
n=
n=
(1.96) 2 (.25) 2
= 96.04 Use 97
(.05) 2
For reporting purposes, the US EIA might decide to round up to a sample size of 100.
39. a.
n=
2
z.025
p (1 − p ) (1.96) 2 (.156)(1 − .156)
=
= 562
E2
(.03) 2
b.
n=
2
z.005
p (1 − p ) (2.576) 2 (.156)(1 − .156)
=
= 970.77 Use 971
E2
(.03) 2
...

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