1. Statistical Reasoning for everyday life
Intro to Probability and Statistics
Mr. Spering – Room 113

2. 8.1 Sampling Distributions
NOTATION AND SYMBOL REVIEW: n…
Sample size μ…
Population mean
σx…
Population standard deviation
Sx…
Sample standard deviation
SAMPLE MEAN

3. 8.1 Sampling Distributions
NOTATION AND SYMBOL REVIEW: z…
Z-score (value compared with mean and σ) r…
Correlation coefficient
∑x…
Sum of x values
P(x)…
Probability of x

4. 8.1 Sampling Distributions
Sampling error…
The error that is introduced when a sample is used to estimate a population. It does not include other sources of error, such as those due to biased sampling, bad survey questions, or recording mistakes.
Would you expect the sampling error to increase or decrease if the sample size were increased?
The sampling error is the observed differences in such things as means and standard deviations, or proportions, from the population from which the sample is taken. If error is truly random it should decrease with sample size C.L.T
If systematic the errors should not change regardless of sample.

5. 8.1 Sampling Distributions
Distribution of Sample Means… (Samples > 30)
The larger the sample size, the more closely the sampling distribution approximates a normal distribution. In all cases, the mean of the sampling distribution equals the population mean. If only one sample is available, its sample mean, is the best estimate for the population mean. (C.L.T.)
EXAMPLE:
Texas has roughly 225,000 farms. The mean farm size is 582 acres. Suppose that for random samples of 100 farms, the distribution of sample means has a mean of 582 acres and a standard deviation of 15 acres. You select a random sample of 100 farms which have a mean size of What is the probability of selecting another sample with a mean greater than 600 acres?

6. 8.1 Sampling Distributions
SAMPLE PROPORTIONS → PERCENTAGES & FRACTIONS
More notations:
Population proportions →
Sample proportions →
Distribution of sample proportions…
The distribution of sample proportions results when we find the proportions in all possible samples of a given size. The larger the sample, the more closely the sampling distribution approximates a normal distribution. In all cases, the mean of the sampling distribution equals the population proportion. If only one sample is available it is the best estimate for the population proportion.

7. 8.1 Sampling Distributions
Class work:
pg 343 # 1-15 all ?