25) Look at the 95% confidence intervals for the variables 10SD1, 50SD1, and 90SD1. a. Identify the interval for 10SD1. b. Identify the interval for 50SD1. c. Identify the interval for 90SD1. d. How does the change to standard deviation of the population effect the confidence interval? Explain. 26) Look at the 95% confidence intervals for the variables 10n1, 100n1, and 1000n1. a. Identify the interval for 10n1. b. Identify the interval for 100n1. c. Identify the interval for 1000n1. d. How does the change in sample size effect the confidence interval? Explain.Calculate 95% Confidence Intervals for the variable Sleep by the variable Gender to estimate the population mean for Males/Females - Select Stat > T Stats > One Sample > With Data. Notice that in this case the t-distribution will be used to create the interval. This gives a more accurate interval as explained in the notes. Under Select column(s): select Sleep. In the Group by: dropdown box select Gender. Click on the Confidence Interval option and for Level: verify 0.95 is entered. Click Compute. Simulating Data and Calculating Confidence Intervals Close out the current worksheet and open a new worksheet by selecting Open StatCrunch. Simulate three samples of size 100 from a normal distribution with a mean of 50 and standard deviations of 10, 50, and 90 - Select Data > Simulate > Normal. In the Rows: textbox enter 100 and in the Columns: textbox enter 1. For the Mean: enter 50 and for the Std. Dev.: enter 10. Under Column name(s): Prefix: enter 10SD. Click Compute. In the window that opens, select Options > Edit. Change the Std. Dev.: to 50 and change the Column name(s): Prefix: to 50SD. Click Compute. Once again select Options > Edit. Change the Std. Dev.: to 90 and change the Column name(s): Prefix: to 90SD. Click Compute. Simulate three samples of size 10, 100, and 1000 from a normal distribution with a mean of 50 and a standard deviation 20 - Select Data > Simulate > Normal. In the Rows: textbox enter 10 and in the Columns: textbox enter 1. For the Mean: enter 50 and for the Std. Dev.: enter 20. Under Column name(s): Prefix: enter 10n. Click Compute. In the window that opens, select Options > Edit. Change the Rows: textbox to 100 and change the Column name(s): Prefix: to 100n. Click Compute. Once again select Options > Edit. Change the Rows: to 1000 and change the Column name(s): Prefix: to 1000n. Click Compute. Calculate 95% Confidence Intervals for the variables 10SD1, 50SD1, 90SD1, 10n1, 100n1, and 1000n1 to estimate the population mean - Select Stat > T Stats > One Sample > With Data. Under Select column(s): select 10SD1, 50SD1, 90SD1, 10n1, 100n1, and 1000nl. Click on the Confidence Interval option and for Level: verify 0.95 is entered. Click Compute. Save this simulated data in StatCrunch - Select Data > Save. Under File Name: enter 'Simulation' and click Save. (The data can be accessed under My Data and you will be able to use this data again in Lab 12)Lab 11 Calculating Confidence Intervals for one Variable Open the Student Survey Data. Calculate a 50% Confidence Interval for the variable State to estimate the proportion of students at BCTC who were born in Kentucky - Select Stat > Proportion Stats > One Sample > With Data. Under Values in: select State and for Success: enter Kentucky (must be typed exactly as displayed in data set). Click on the Confidence interval for p option and for Level: enter 0.5. Click Compute. Calculate a 90% Confidence Interval for the variable State to estimate the proportion of students at BCTC who were born in Kentucky - Select Stat > Proportion Stats > One Sample > With Data. Follow the same steps as above except for Level: enter 0.9. Click Compute. Calculate a 95% Confidence Interval for the variable State to estimate the proportion of students at BCTC who were born in Kentucky - Select Stat > Proportion Stats > One Sample > With Data. Follow the same steps as above except for Level: enter 0.95. Click Compute. Calculate a 99% Confidence Interval for the variable State to estimate the proportion of students at BCTC who were born in Kentucky - Select Stat > Proportion Stats > One Sample > With Data. Follow the same steps as above except for Level: enter 0.99. Click Compute. Calculate 95% Confidence Intervals for the variable Subject by the variable Gender to estimate the proportion of Males/Females at BCTC who choose Math as their favorite subject -Select Stat > Proportion Stats > One Sample > With Data. Under Values in: select Subject and for Success: enter Math (must be typed exactly as displayed in data set). In the Group by: dropdown box select Gender. Click on the Confidence interval for p option and for Level: verify 0.95 is entered. Click Compute. Calculate a 95% Confidence Interval for the variable Temp to estimate the population mean - Select Stat > Z Stats > One Sample > With Data. Under Select column(s): select Temp. Click on the Confidence Interval option and for Level: verify 0.95 is entered. Click Compute.SHORT ANSWER WRITING ASSIGNMENT 19) In order to conduct inferential statistics the sample must be representative of the population. For lab purposes, we will assume that our sample of students is representative of the student body at BCTC. Is this the case? Explain. 20) Look at the 50% confidence interval for the population proportion of students who were born in Kentucky. a. Identify the interval. b. Explain why a 50% interval would not be of much use in estimating the population proportion. 21) Give the following confidence intervals for the population proportion of students who were born in Kentucky. a. 90% confidence interval b. 95% confidence interval c. 99% confidence interval d. What happens to the interval as the confidence level increases? Explain. 22) Look at the 95% confidence intervals for the population proportion of males/females who choose math as their favorite subject. a. Identify the interval for males. b. Interpret the interval for males. c. Identify the interval for females. d. Interpret the interval for females. 23) Look at the 95% confidence interval for the population mean of the variable Temp. a. Identify the interval. b. Interpret the interval. 24) Look at the 95% confidence intervals for the population means of the variable Sleep grouped by Gender. a. Identify the interval for males. b. Interpret the interval for males. c. Identify the interval for females. d. Interpret the interval for females