Statistics 101: Section L - Laboratory 3 The first activity in today’s lab requires you to use your calculator to compute sample statistics, the sample mean and sample standard deviation. The other activities look at data to see if we can decide if they came from a normally distributed population. Activity 1: The predicted high temperatures for Ames for Jan. 12 -18, 2004 are: 39, 36, 29, 22, 27, 25, 36 Use your calculator to compute the sample mean predicted high temperature and the sample standard deviation of the predicted high temperatures. If you do not know how your calculator works the lab instructor or I may be able to help. Activity 2: You have JMP output for 3 samples of data, Data Set #1, Data Set #2 and Data Set #3. Each data set contains 100 observations. These observations were generated from different density curves. You are to determine if the normal density curve or some other density curve was used to generate each sample data set. In other words, could the data in each set have come from a population with a normal distribution? Since the data sets are generated from known density curves, the population means and standard deviations are known. The values of µ and σ are given in the table below. Data Set #1 #2 #3 Population µ σ 1 1 5 1 50 1 For each data set, answer the following questions. 1. Describe the shape of the histogram? What does this indicate about the probable shape of the density curve? 2. What is the overall pattern for the normal quantile plot? What does this indicate about whether the data are generated from a normal density curve? 3. If the normal density curve was is used to generate a data set, the 68-95-99.7 rule should apply, roughly, to the 100 observations. Using µ and σ from the table above, determine what percentage of the 100 observations are within 1, 2 and 3 standard deviations of the population mean. What does this indicate about the probable shape of the density curve? 4. Based on our answers to the questions 1-3 above, do you believe the normal density curve was used to generate the 100 observations in the data set? Explain your answer. Activity 3: You have JMP output for three sample data sets, the total weight, the net weight of the contents, and the number of M&Ms in fun size bags. We want to decide for each data set if the values could have come from a population with a normal distribution. For each data set, answer the following questions. 1. Describe the shape of the histogram? What does this indicate about the probable shape of the density curve? 2. What is the overall pattern for the normal quantile plot? What does this indicate about whether the data come from a population with a normal distribution? 3. Why can’t we check the 68-95-99.7 rule in the same way we did in Activity 2? 4. Using your answers to questions 1 and 2 above, do you believe that the sample data could have come from a population that is normally distributed? Explain your answer.