Popular in Statistics for Biosciences
Popular in Statistics
verified elite notetaker
This 5 page Class Notes was uploaded by Mile on Monday October 26, 2015. The Class Notes belongs to STP 231 at Arizona State University taught by in Fall 2015. Since its upload, it has received 53 views. For similar materials see Statistics for Biosciences in Statistics at Arizona State University.
Reviews for Leson
I'm a really bad notetaker and the opportunity to connect with a student who can provide this help is amazing. Thank you so much StudySoup, I will be back!!!
Report this Material
What is Karma?
Karma is the currency of StudySoup.
Date Created: 10/26/15
Sampling Error 0 Sampling error An error that occurs when we use samples to estimate a population characteristic Defining Sampling Distribution 0 Sampling distribution of a statistic Probability distribution that specifies probabilities for all possible values the statistic can take 0 Capital X is now a statistic or sampling distribution of sample mean Simple Illustrative Example 0 The random variable of the population is the number of meals per day A population consists of 4 people Number of meals per day 1 3 5 and 7 The population mean Construct the sampling distribution of the sample mean for Samples IU39ICJO a random samples of size 1 b random samples of size 2 c random samples of size 3 d random samples of size 4 e For sample of each size find the probability the sample mean will be equal to the population mean D For sample of each size find the probability the sampling error made in estimating the population mean by the sample mean will be 1 or less Using the number 1 3 5 7 I n 1 I X 2 sample mean Sampling distribution is made up of the sample mean and probability Sample mean Probability 1 14 3 14 5 14 7 14 o All possible samples when sample size is 2 n2 0 1 3 o 1 5 o 1 7 O 3 5 O 3 7 O 5 7 Samples Sample mean Probability 13 2 16 15 3 16 17 4 16 35 4 16 37 5 16 57 6 16 0 Could combine the samples 17 and 35 0 Their probability would become 26 or 13 0 Sampling distribution of sample mean X Probability 2 16 3 16 4 13 5 16 6 16 Sampling distribution of sampling mean for sample sizes of 3 n3 Samples Sample Mean Probability 135 3 14 137 113 36667 14 157 133 43333 14 357 5 14 0 Remember average or mean is addition of all values and divided by number of values 0 Allvalues1359 0 Number of Values 3 I 93 3 For sample size 4 0 There is only one possible sample 135 The sample mean is 4 0 We can obtain population standard deviation I ll 2 4 u o 2 Square root of Zxi u2 N u 2236068 39 HXbar 4 lJ I O39X bar 1290994 uxbar is the mean of the sample mean oxbar is the standard deviation of the sample mean u The quotXquot in Xbar is capitalized This is because it is treating the sample mean as a random variable Square root of NnN1 oSqrtn For this problem I Sqrt4241 2236068Sqrt2 Our Findings 0 HXbar 4 lJ o oxbar Square root of NnN1 oSqrtn 0 Where N4 n1 2 3 4 I 4 022236068 Sample size HXbar GXbar 1 4 2236068 2 4 1290994 3 4 0745356 4 4 0 Sampling Distribution of the Sample Mean 0 Suppose the population mean is u and population standard deviation is G then the sampling distribution of the sample mean has mean ux bar u and standard deviation oxbar oSqrtn 0 When population reaches sample size their values become exactly the same Example 0 Based on census information The total income in a household in Ohio has a mean of 46000 and a standard deviation of 10000 0 For samples of size 100 find the mean and standard deviation of all possible sample means Solution 0 For the sampling distribution of the sample mean the center is 46000 and the variability is 10000sqrt100 1000 Central Limit Theorem 0 For random sample of sufficiently large size the sampling distribution of the sample mean is approximately normal with mean u and standard deviation osqrtn Central Limit Theorem Conditions 0 Randomization Data values must be sampled randomly 0 Independence assumption The sampled values must be mutually independent 0 10 rule The sample is no more than 10 of the population Large enough sample 0 The sample size must be at least 30 u If we were to draw a curve to fit the information it will be a symmetric normal curve Each number represents a sample mean of one of the many samples selected I When we put all of these sample means together we make the sample normal distribution curve Follows 39 llXbar I GXbar