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Unformatted text preview: sample size. In our
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:
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
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
• 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 )
– is referred to as the standard error of the proportion.
σp ECO 3411 42 Example: UCF
• Sampling Distribution of pfor In-State Residents
• Recall that 72% of the prospective students applying to
UCF desire on-campus housing.
• What is the probability that a simple random sample of 30
applicants will provide an estimate of the population
proportion of applicants desiring on-campus housing that
is within plus or minus .05 of the actual population
In other words, what is the probability that
will be between .67 and .77? ECO 3411 43 Example: UCF
• Sampling Distribution of p for In-State Residents .72(1 − .72)
30 E( p ) = .72 ECO 3411 44 Example:UCF
• Sampling Distribution of p for In-State 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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This note was uploaded on 01/17/2014 for the course ECO 3411 taught by Professor Staff during the Winter '08 term at University of Central Florida.
- Winter '08