STAT 200 LAB 3 2 UNDERSTANDING AND INTERPRETING CONFIDENCE INTERVALS STAT 200 Lab Activity for Section 3 2 Understanding and Interpreting Confidence Intervals Learning Objectives Identify the parameter being estimated and the sample statistic that gives the best estimate Construct a confidence interval for a parameter based on a sample statistic and margin of error Use a confidence interval to recognize plausible values of the population parameter Construct a confidence interval for a parameter given a sample statistic and an estimate of the standard error Interpret in context what a confidence interval says about a population parameter Activity 1 Sample from a population to build a confidence interval The virtual bead box choose Bead Box for Lab 3 2 represents voters in a medium size town The color of each bead represents each individual s opinion for or against on a ballot proposition about property taxes Assume the election is in one week and we are interested in estimating support for the proposition Let yellow beads triangles be in support and green beads squares be against NOTE Make sure you calculate the statistic for Yellow beads The website provides the proportion for the green beads In this activity we will learn about the people s opinions by taking a sample from the population and building a confidence interval for the proportion of town voters in favor of the ballot proposition 1 Which parameter are we interested in Use proper notation 2 Take a sample from the bead box and use your sample to calculate the appropriate sample statistic for the yellow beads Use proper notation 3 It is known that the standard error for this sample statistic is 0 0837 Use this fact to build a 95 confidence interval for the parameter 4 Interpret your confidence interval in context Refer to lecture slides if needed We are 95 blank1 that the blank2 proportion of voters in favor of the proposition is between blank3 blank 4 12 15 25 University 2025 The Pennsylvania State STAT 200 LAB 3 2 UNDERSTANDING AND INTERPRETING CONFIDENCE INTERVALS 5 Based on your confidence interval can you say with 95 certainty that the proposition about property taxes will pass on Election Day Activity 2 Building confidence intervals for Hollywood movie budgets A sampling distribution is shown for budgets in millions of dollars of all movies to come out of Hollywood in 2011 using samples of size n 20 We see that the standard error is about 10 232 For each of the sample means listed below a Find their location in the sampling distribution in the figure above b Use the standard error of 10 232 to find the 95 confidence interval to c Also indicate whether the confidence interval successfully captures the true estimate the population mean population mean of 53 481 million dollars 1 x 42 2 x 67 3 x 85 12 15 25 University 2025 The Pennsylvania State STAT 200 LAB 3 2 UNDERSTANDING AND INTERPRETING CONFIDENCE INTERVALS Activity 3 Sample size and confidence intervals For this activity we will use the students in all STAT 200 classes in a semester as our population The data set GPA csv is the file containing responses to the student survey We will use this population to investigate the relationship between sample size standard error and width of confidence intervals Let s consider the variable GPA In StatKey under Sampling Distributions select mean Choose upload file to upload the GPA csv data and select the correct variable GPA Report all quantities to two decimal places to make the calculations friendlier 1 Using a sample size of n 10 generate a sampling distribution with at least 5000 samples a Where is the center of this sampling distribution b What is the standard error c If we were to build a 95 confidence interval using one of the sample means how wide would it be 2 Now using a sample of size n 50 generate a sampling distribution with 5000 samples a Where is the center of this sampling distribution b What is the standard error c If we were to build a 95 confidence interval using one of the sample means how wide would it be 3 Finally using a sample of size n 100 generate a sampling distribution with 5000 samples a Where is the center of this sampling distribution b What is the standard error c If we were to build a 95 confidence interval using one of the sample means how wide would it be 2025 The Pennsylvania State 12 15 25 University STAT 200 LAB 3 2 UNDERSTANDING AND INTERPRETING CONFIDENCE INTERVALS 4 What happens to the center of the distribution as the sample size increases 5 What happens to the standard error and the width of confidence intervals as the sample size increases Activity 4 Interpreting a confidence interval Page 222 in our textbook is helpful Using a sample of 24 deliveries described in Diary of a Pizza Girl on the Slice website we find a 95 confidence interval for the mean tip given for a pizza delivery in her area to be 2 18 to 3 90 Which of the following is a correct interpretation of this interval 1 2 95 of all pizza delivery tips will be between 2 18 and 3 90 3 4 5 I am 95 sure that all pizza delivery tips will be between 2 18 and 3 90 I am 95 sure that the mean pizza delivery tip for this sample will be between 2 18 and 3 90 I am 95 sure that the mean tip for all pizza deliveries in her area will be between 2 18 and 3 90 I am 95 sure that the confidence interval for the mean pizza delivery tip will be between 2 18 and 3 90 Activity 5 Election Day from Activity 1 1 The results are in The proposition passed with 69 6 of the vote Did your confidence interval contain the true value for the population parameter Note that yes and no are both right here as long as it accurately reflects your confidence interval 2 Assuming your instructor has 600 students that will perform this experiment today each using a sample size of 30 How many of the students do you expect to have calculated confidence intervals that contain the true value for the population parameter at 95 confidence a What about for a class of 400 b What about for a class of 200 12 15 25 University 2025 The Pennsylvania State