Question

Use Excel to standard normal observations with assumed population parameters with mean 16 and standard deviation 5. Go to Data Analysis (you need to have chosen "Analysis Toolpack" first) -> Random Number Generation -> Normal. Generate one random variable with numbers generated for samples of size 5, 16, and 25 from the default standard normal distribution. This will simulate the importance of the "assume normal" assumption. Use the =) provided from the parent population as your "assumed" population standard deviation. Create confidence intervals at 85% and 96% confidence levels for each case. Do you end up with any confidence intervals not including the population mean? What happens as you vary the confidence and sample sizes.

Answer 1

*svn 85 % Confidence Interval is = Ã E Z 0.15 Critical Value Za2 = -1.439531 = 1.44 Lower limit = x - 202*svn =16-1.44*575 12.7801 Upper limit = x +702*svn =16+1.44*575 19.2199 85 % Confidence interval is =( 12.7801 , 19.2199) 16 85 % Confidence Interval is = x + 2)*syn 0.15 Critical Value Za2 = -1.439531 = 1.44 Lower limit = x - Za*svn =16-1.44*5/16 14.2000 Upper limit = x + Zn*syn =16+1.44*5716 17.8000 85 % Confidence interval is =( 13.55, 18.45)

85 % Confidence Interval is = 2)*syn a = 0.15 Critical Value Za2 = -1.439531 = 1.44 Lower limit = x - 72*svn =16-1.44*5725 14.5600 Upper limit = x + Zuz*sVn =16+1.44*5725 17.4400 85 % Confidence interval is =( 14.56, 17.44)

96% confidence interval

96 % Confidence Interval is = Ž EZsyn 0.04 Critical Value 2012 = -2.053749 = 2.05 Lower limit = x - Zu2*svn =16-2.05*515 11.4161 Upper limit = x + Zu2*syn =16+2.05*5V5 20.5839 96 % Confidence interval is =( 11.4161 , 20.5839) 16 96 % Confidence Interval is = x + 2x2*svn a. = 0.04 Critical Value ZQ2 = -2.053749 = 2.05 Lower limit = X - 202*svn =16-2.05*5V16 = 13.4375 Upper limit = * +22*svn =16+2.05*5/16 = 18.5625 96 % Confidence interval is =( 13.4375, 18.5625)

96 % Confidence Interval is = 2*svn 0.04 Critical Value -2.053749 Za/2 = 205221 = 2.05 Lower limit = x - 7,2*svn =16-2.05*5725 13.9500 Upper limit = * + Zw2*svn =16+2.05*5725 = 18.0500 96 % Confidence interval is =( 13.95, 18.05)
For increasing sample size the width of the confidence interval was decreased