Unformatted text preview: sample size. In our
x
x example, E( ) remains at 990. Whenever the sample size is increased, the standard
σx error of the mean is decreased. With the increase in the sample size to n = 100, the standard error of the mean is decreased to:
σ
80
σx =
=
= 8.0
n
100 ECO 3411 37 Relationship Between the Sample Size
and the Sampling Distribution of x
With n = 100,
σ x = 8
With n = 30,
σ x = 14.6 E( x ) = 990
ECO 3411 x
38 Relationship Between the Sample Size
x and the Sampling Distribution of Recall that when n = 30, P(980 < < 1000) = .5034.
x We follow the same steps to solve for P(980 < x 1000)
< when n = 100 as we showed earlier when n = 30. Now, with n = 100, P(980 < < 1000) = .7888.
x Because the sampling distribution with n = 100 has a
x smaller standard error, the values of have less variability and tend to be closer to the population
x mean than the values of with n = 30. ECO 3411 39 Relationship Between the Sample Size
x and the Sampling Distribution of Sampling
Distribution
x
of σx = 8 Area = .7888 980 990 1000
ECO 3411 x
40 Sampling Distribution of p
• The sampling distribution of p is the probability
distribution of all possible values of the sample proportion
p p
• Expected Value of E ( p) = p where:
p = the population proportion ECO 3411 41 Sampling Distribution of
• Standard Deviation of σp = p p Infinite Population ONLY p (1 − p )
n –
– is referred to as the standard error of the proportion.
σp ECO 3411 42 Example: UCF
• Sampling Distribution of pfor InState Residents
• Recall that 72% of the prospective students applying to
UCF desire oncampus housing.
• What is the probability that a simple random sample of 30
applicants will provide an estimate of the population
proportion of applicants desiring oncampus housing that
p
is within plus or minus .05 of the actual population
proportion?
In other words, what is the probability that
will be between .67 and .77? ECO 3411 43 Example: UCF
• Sampling Distribution of p for InState Residents .72(1 − .72)
σp =
= .082
30 E( p ) = .72 ECO 3411 44 Example:UCF
• Sampling Distribution of p for InState Residents
Sampling distribution of p
Area = .2291 Area = .2291 0.67 0.72 0.77 p For z = .05/.082 = .61, the...
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 Winter '08
 Staff
 Point Estimators

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