Statistics 20: Quiz 4 Solutions
1. A team of doctors want to estimate the life expectancy of students afflicted with the rare
genetic disease
statinotisticitis
; however, only 15 known cases have ever been diagnosed. The
sample reported a mean lifespan of 95 years with a standard deviation of 10.
The doctors
believe it’s reasonable to assume a Normal distribution for each data point. Construct a 95%
confidence interval for life expectancy of patients with this disease.
We may consider the life spans reported in the
n
= 15 known cases of the disease to be ran
dom variables
X
1
, . . . , X
15
that are independent copies of
X
∼
N
(
μ, σ
2
). We are interested in
learning the life expectancy (or mean lifespan)
μ
. However, in this case the data’s standard
deviation
σ
is unknown; the reported numbers for the mean and standard deviation are the
estimates
¯
X
and
S
. (It would indeed be difficult to know anything beyond these estimates
when only 15 cases have ever been reported.) Because
n
is small,
σ
is unknown, and each data
point follows a Normal distribution, we must use the
t
distribution with
n

1 = 15

1 = 14
degrees of freedom to construct a 95% confidence interval:
95% CI for
μ
=
¯
X
±
t
14
df
0
.
95
S
√
n

1
= 95
±
2
.
14
10
√
15

1
= (89
.
281
,
100
.
719).
2. A veterinarian wants to estimate the mean weight of fullgrown calico cats. A previous study
suggests assuming an SD of 3 pounds is reasonable. How many calicos should be surveyed
to ensure with probability 0
.
95 that the maximum error is less than 0.1 pounds? (Round a
decimal result up.)
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 Spring '08
 Staff
 Statistics, Normal Distribution, Standard Deviation, Null hypothesis, Probability theory

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