Confidence Interval

Question

Use the sample values listen below to construct a 95% confidence interval estimate of the population mean. assume that the population has a normal distribution

 

51 63 36 43 34 62 73 39 53 79

Answer 1

Sample: [34, 36, 39, 43, 51, 53, 62, 63, 73, 79]

 

N=10

 

Sum=533

 

Mean=533/10=53.3

 

Standard deviation=15.65

 

Standard Error= SE = standard deviation / sqrt( n )=15.65/square root of 10=

15.65/3.16=4.95

 

Critical value (from t table, degrees of freedom=n-1=9) 2.262

 

Margin of error=critical value*standard error*0.95=2.262*4.95*0.95=10.63

 

CI95=53.3+ or - 10.63 or (42.67, 63.93)