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L1 chapter 7 new(1)

5034 x wefollowthesamestepstosolveforp980x 1000

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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 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 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 In-State Residents .72(1 − .72) σp = = .082 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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