Statistics 200_ Lab Activity for Sections 3.1

Activity 0 This lab uses StatKey . Open the StatKey guide available on Canvas. Activity 1: Creating a sampling distribution. To complete this activity, you will use a virtual box of small colored beads . As a class, we are going to build a sampling distribution for the proportion of blue beads in the box. 1. Open the virtual box by choosing ‘Bead Box for Lab 3.1’ in the left menu after opening the link above. What is the population? 2. By just looking at the picture of the virtual box, what do you think the proportion of blue beads is? a. 3. Now take a random sample of n = 30 beads from the box. Each student must take their own sample, even if you’re working in a group! To take a sample just click the draw a sample button. You may want to save a screenshot of your sample for future reference. Using this sample, what is the sample proportion? Your answer should be correctly rounded to two decimal places, i.e. 0.xx. - 0.57 1. Now what do you think the proportion of blue beads in the box is? Has your answer changed from question 2? a. 2. Enter your sample proportion using the Canvas link in the activities page for this section. It is very important that you do this so that you and your classmates can create a sampling distribution to discuss in the last activity. 3. Discuss with the other people in your lab group about how different your sample proportions were. Activity 2: Which parameter, which statistic? 1. A random sample of n = 461 smartphone users in the US in January 2015 found that 355 of them have downloaded at least one app. a. Give notation for the parameter of interest and define the parameter in this context. i. Population of people with one app downloaded a. Give notation for the quantity that gives the best estimate for this parameter and give its value. i. 355/461 1. Of the n = 355 smartphone users in question 1 who had downloaded an app, the average number of apps downloaded was 19.7. a. Give notation for the parameter of interest and define the parameter in this context. i. Mu a. Give notation for the quantity that gives the best estimate for this parameter and give its value. i. 355 is mu and 19.7 is x-bar 1. For questions 1 and 2 above, what would we have to do to calculate the parameters exactly? a. You have to estimate, you cannot calculate the parameter exactly 1. Florida has over 7,700 lakes. We wish to estimate the correlation between the pH levels of all Florida lakes and the mercury levels of fish in the lakes. The correlation between these two variables for a sample of n = 53 lakes is -0.575. a. Give notation for the parameter of interest and define the parameter in this context. i. rho a. Give notation for the quantity that gives the best estimate for this parameter and give its value. i. Correlation - r (-0.575)

1. A study wants to investigate whether regular exercise leads to a lower resting heart rate. A random sample of Stat 200 students were classified as either “no” or “yes” regarding regular exercise. For the “no” group (group 1) the average resting heart rate was 72.0 beats/minute and for the “yes” group (group 2) the average resting heart rate was 65.2 beats/minute. a. Give notation for the parameter of interest and define the parameter in this context. i. M1 - m2 (two different means) a. Give notation for the quantity that gives the best estimate for this parameter and give its value. i. Xbar 1 - xbar 2 ii. 72 bpm - 65.2 = 6.8 Activity 3: Beads revisited: our sample results and implications of sample size Observe the dataset of sample proportions generated by you and your classmates. You can find the dataset following the link on Canvas in the submodule for this section. Download as a CSV file and then upload that CSV file into Minitab. (File > Open Worksheet) 1. Use Minitab to create a dotplot of the sample proportions. (Graph > Dotplot) 2. Observe this dotplot of sample proportions: a. What does each dot represent? i. Dots represent the cases which are the people a. What is the shape of this sampling distribution? Where is the center? i. Bell shaped, center is at .55 a. Recall that the standard error for a sample statistic is the standard deviation of the sampling distribution. Use Minitab to find the standard error of your estimate from Activity 1. (Hint: find the standard deviation of the class dataset of sample proportions). i. 0.005 1. What is your best guess for the population proportion of blue beads in that bead box? a. 400/800 = ½ 1. Assuming that your answer for Question 3 above is in fact the correct population proportion, let’s investigate how the sampling distribution would change if we had taken larger or smaller samples. Instead of taking more samples from the bead box, we will use StatKey to simulate this process. The program will randomly generate many samples (and sample proportions) from a pre-determined population. ( StatKey > Sampling Distributions > Proportion) a. Generate a single sample of size n = 100 from a population with the proportion you specified in question 3 [Edit Proportion > enter your value from question 3 and press the button labeled “Generate One Sample”]. What was the sample proportion? i. 0.45 a. Now generate at least 2000 sample proportions and observe the sampling distribution dotplot. Hint: Use the “Generate 1000 samples” button twice. a. What does each dot represent? i. Cases a. Where is the center of the sampling distribution? i. 0.499 a. What is the standard error of the sample proportion with size n = 100? i. 0.051 1. Finally, create a sampling distribution from the same population (same proportion) but with samples of size n = 200, with at least 2000 samples. a. What is the standard error? i. 0.035 a. Where is the center of the distribution?