Math 140 Notes and Activity Packet (Word) Sampling Variability, Sampling Distributions, Standard Error and Confidence Intervals Confidence Intervals Act 1 Exploring Sampling Variability for Mean Averages with a Sampling Distribution The goal of this activity is to explore how well random samples approximate population values. Normally we do not know population values and we must use a sample value to approximate the population value. This is called a “point estimate”. For this activity we will look at some population data from International Coffee Organization (ICO). We will be using the “Columbian Mild” price data in U.S. cents per pound. The population mean average price was 134.338 cents per pound. Again, in real data analysis we often do not know the population value, but for this activity it is useful for comparison purposes. Open the “Confidence Interval Act 1 Data Set A” in Excel. 81 random samples have been taken from the Columbian Mild data. All the data sets have 30 coffee prices. Each person in the class will be finding the mean of a few of these data sets. Once you find the mean, you will put a magnet up or draw a dot on the board to represent the sample mean you found. When everyone’s magnets or dots are up on the board, we will have generated a “sampling distribution”. Answer the following questions: 1. The population mean was 134.338 cents. How many cents was the sample mean you calculated from the population mean of 134.338 cents? (If you calculated more than one sample mean, answer the question for all the sample means you calculated.) 2. Look at the dots or magnets on the board. Did all the sample means come out to be the same as the population mean of 134.338 cents? Why do you thing this happened? Aren’t random samples supposed to be good approximations of the population? What does this tell you about sampling variability? 3. Normally we may have only one random sample. If all you knew was one of the random samples on the board, how difficult would it be to determine that the population mean is really 134.338 cents? What does this tell us about the difficulty in determining population values from 1 random sample?
Math 140 Notes and Activity Packet (Word) Sampling Variability, Sampling Distributions, Standard Error and Confidence Intervals Confidence Intervals Act 1 Exploring Sampling Variability for Mean Averages with a Sampling Distribution The goal of this activity is to explore how well random samples approximate population values. Normally we do not know population values and we must use a sample value to approximate the population value. This is called a “point estimate”. For this activity we will look at some population data from International Coffee Organization (ICO). We will be using the “Columbian Mild” price data in U.S. cents per pound. The population mean average price was 134.338 cents per pound. Again, in real data analysis we often do not know the population value, but for this activity it is useful for comparison purposes. Open the “Confidence Interval Act 1 Data Set A” in Excel. 81 random samples have been taken from the Columbian Mild data. All the data sets have 30 coffee prices. Each person in the class will be finding the mean of a few of these data sets. Once you find the mean, you will put a magnet up or draw a dot on the board to represent the sample mean you found. When everyone’s magnets or dots are up on the board, we will have generated a “sampling distribution”. Answer the following questions: 1. The population mean was 134.338 cents. How many cents was the sample mean you calculated from the population mean of 134.338 cents? (If you calculated more than one sample mean, answer the question for all the sample means you calculated.) 2. Look at the dots or magnets on the board. Did all the sample means come out to be the same as the population mean of 134.338 cents? Why do you thing this happened? Aren’t random samples supposed to be good approximations of the population? What does this tell you about sampling variability? 3. Normally we may have only one random sample. If all you knew was one of the random samples on the board, how difficult would it be to determine that the population mean is really 134.338 cents? What does this tell us about the difficulty in determining population values from 1 random sample?