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Sampling and Sampling Distributions: Part 2 •Sample size and the sampling distribution of •Sampling distribution of •Sampling methods x p
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### Transcript of Sampling and Sampling Distributions: Part 2 Sample size and the sampling distribution of Sampling...

• Slide 1
• Sampling and Sampling Distributions: Part 2 Sample size and the sampling distribution of Sampling distribution of Sampling methods
• Slide 2
• Relationship Between the Sample Size and the Sampling Distribution of and the Sampling Distribution of Suppose we select a simple random sample of 100 Suppose we select a simple random sample of 100 applicants instead of the 30 originally considered. applicants instead of the 30 originally considered. E ( ) = regardless of the sample size. In our E ( ) = regardless of the sample size. In our example, E ( ) remains at 990. example, E ( ) remains at 990. Whenever the sample size is increased, the standard Whenever the sample size is increased, the standard error of the mean is decreased. With the increase error of the mean is decreased. With the increase in the sample size to n = 100, the standard error of the in the sample size to n = 100, the standard error of the mean is decreased to: mean is decreased to:
• Slide 3
• Relationship Between the Sample Size and the Sampling Distribution of and the Sampling Distribution of With n = 30, With n = 100,
• Slide 4
• Recall that when n = 30, P (980 < < 1000) =.5034. Recall that when n = 30, P (980 < < 1000) =.5034. Relationship Between the Sample Size and the Sampling Distribution of and the Sampling Distribution of We follow the same steps to solve for P (980 < < 1000) We follow the same steps to solve for P (980 < < 1000) when n = 100 as we showed earlier when n = 30. when n = 100 as we showed earlier when n = 30. Now, with n = 100, P (980 < < 1000) =.7888. Now, with n = 100, P (980 < < 1000) =.7888. Because the sampling distribution with n = 100 has a Because the sampling distribution with n = 100 has a smaller standard error, the values of have less smaller standard error, the values of have less variability and tend to be closer to the population variability and tend to be closer to the population mean than the values of with n = 30. mean than the values of with n = 30.
• Slide 5
• Relationship Between the Sample Size and the Sampling Distribution of and the Sampling Distribution of1000980990 Area =.7888 SamplingDistributionof
• Slide 6
• A simple random sample of n elements is selected from the population. Population with proportion p = ? n Making Inferences about a Population Proportion The sample data provide a value for the sample proportion. The value of is used to make inferences about the value of p. Sampling Distribution of
• Slide 7
• where: p = the population proportion The sampling distribution of is the probability distribution of all possible values of the sample proportion. Expected Value of
• Slide 8
• is referred to as the standard error of the is referred to as the standard error of the proportion. Sampling Distribution of Finite Population Infinite Population Standard Deviation of
• Slide 9
• The sampling distribution of can be approximated The sampling distribution of can be approximated by a normal probability distribution whenever the by a normal probability distribution whenever the sample size is large. sample size is large. The sample size is considered large whenever these The sample size is considered large whenever these conditions are satisfied: conditions are satisfied: np > 5 n (1 p ) > 5 and Sampling Distribution of
• Slide 10
• For values of p near.50, sample sizes as small as 10 permit a normal approximation. With very small (approaching 0) or very large (approaching 1) values of p, much larger samples are needed. Sampling Distribution of
• Slide 11
• For our example, with n = 30 and p =.72, the normal probability distribution is an acceptable approximation because: Sampling Distribution of for the Proportion of Applicants Wanting On-Campus Housing of Applicants Wanting On-Campus Housing n (1 - p ) = 30(.28) = 8.4 > 5 and np = 30(.72) = 21.6 > 5
• Slide 12
• Sampling Distribution of for the Proportion of Applicants Wanting On-Campus Housing of Applicants Wanting On-Campus Housing SamplingDistributionof
• Slide 13
• What is the probability that a simple random sample 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 proportion? In other words, what is the probability that will be In other words, what is the probability that will be between.67 and.77? Sampling Distribution of for the Proportion of Applicants Wanting On-Campus Housing of Applicants Wanting On-Campus Housing
• Slide 14
• Sampling Distribution of for the Proportion of Applicants Wanting On-Campus Housing of Applicants Wanting On-Campus Housing Step 1: Calculate the z -value at the upper endpoint of the interval. the interval. z = (.77 -.72)/.082 =.61 P ( z