Name: Lab 5: Chapter 6 READ THIS: In the material for the first exam, you learned about the difference between a population and a sample. There is a parameter for the whole population (for example the average age for all U.S. residents), but it would be too difficult, time-consuming, and expensive for us to get the number directly through a census. Instead, we choose to take a random sample and calculate a statistic as an estimate for the population parameter. However, we also know that every time we take a random sample from the population, we will get a different sample statistic simply due to random variability (sampling variability). When we use a statistical technique called inference, we are taking into account random variability when we estimate the population parameter from the sample using a sample statistic (such as X ). Confidence intervals and hypothesis testing are types of inference. 1. (5 points) Using the diagram below, fill in the blanks with these terms: inference, sampling, , , s, . x Population Sample 1 Confidence Intervals Using Internet Explorer or other web browser you prefer to use, go to the website for your textbook: http://bcs.whfreeman.com/ips8e. Click on \"Applets\" and then on \"Statistical Applets: Confidence Intervals.\" Read the explanation at the top of the webpage. Use the 95% confidence level until you are told to change. 2. (2 points) What does the stand for? ____________________ 3. (2 points) When we calculate a confidence interval in real-life (non-applet) circumstances, do we know what is? Circle your answer: Yes No Press the \"SAMPLE\" button to create a single confidence interval. Did your confidence interval from your single sample include the true population mean? Circle your answer: Yes No 4. (3 point) What does the dot in the middle of the confidence interval represent? (Answer with a symbol and in words.) Try creating some more confidence intervals by hitting the \"sample\" button several more times. Check to see if all of your confidence intervals include the true population mean. If you create 100 confidence intervals (click on sample 25 four times), what percentage of your confidence intervals do contain the true population mean (Check the Percent hit value right above the red \"RESET\" button)? _____________% of the confidence intervals contain the true population mean. Now try changing the confidence level and observe the results to your intervals. 5. (2 points) As the confidence level increases, the width of the interval (circle one): increases / decreases / stays the same 6. (2 points) As the confidence level increases, the percentage of intervals which contain the true population mean (circle one): increases / decreases / stays the same 2 Remember, the formula for the confidence interval for the population mean when the population standard deviation is known is: x z =( x z , x + z ) n n n 7. (2 points) As the sample size increases, the width of the interval (circle one): increases / decreases / stays the same. 8. (2 points) As the confidence level increases, the center of the interval (circle one): moves right / moves left / stays the same. 3 Name: Lab 5: Chapter 6 READ THIS: In the material for the first exam, you learned about the difference between a population and a sample. There is a parameter for the whole population (for example the average age for all U.S. residents), but it would be too difficult, time-consuming, and expensive for us to get the number directly through a census. Instead, we choose to take a random sample and calculate a statistic as an estimate for the population parameter. However, we also know that every time we take a random sample from the population, we will get a different sample statistic simply due to random variability (sampling variability). When we use a statistical technique called inference, we are taking into account random variability when we estimate the population parameter from the sample using a sample statistic (such as ). Confidence intervals and hypothesis testing are types of inference. 1. (5 points) Using the diagram below, fill in the blanks with these terms: inference, sampling, , , s, x . Population Sample 1 Confidence Intervals Using Internet Explorer or other web browser you prefer to use, go to the website for your textbook: http://bcs.whfreeman.com/ips8e. Click on \"Applets\" and then on \"Statistical Applets: Confidence Intervals.\" Read the explanation at the top of the webpage. Use the 95% confidence level until you are told to change. 2. (2 points) What does the stand for? ____________________ 3. (2 points) When we calculate a confidence interval in real-life (non-applet) circumstances, do we know what is? Circle your answer: Yes No Press the \"SAMPLE\" button to create a single confidence interval. Did your confidence interval from your single sample include the true population mean? Circle your answer: Yes No 4. (3 point) What does the dot in the middle of the confidence interval represent? (Answer with a symbol and in words.) Try creating some more confidence intervals by hitting the \"sample\" button several more times. Check to see if all of your confidence intervals include the true population mean. If you create 100 confidence intervals (click on sample 25 four times), what percentage of your confidence intervals do contain the true population mean (Check the Percent hit value right above the red \"RESET\" button)? _____________% of the confidence intervals contain the true population mean. Now try changing the confidence level and observe the results to your intervals. 5. (2 points) As the confidence level increases, the width of the interval (circle one): increases / decreases / stays the same 6. (2 points) As the confidence level increases, the percentage of intervals which contain the true population mean (circle one): increases / decreases / stays the same 2 Remember, the formula for the confidence interval for the population mean when the population standard deviation is known is: = ( , + ) 7. (2 points) As the sample size increases, the width of the interval (circle one): increases / decreases / stays the same. 8. (2 points) As the confidence level increases, the center of the interval (circle one): moves right / moves left / stays the same. 3