Question

A recent study of home internet access reported the following number of hours of internet access per month for a sample of 20 persons [3+4+4+2 points]. 74 81 83 72 76 71 63 66 68 78 76 66 87 54 82 86 90 98 58 92 (a) Use probability plot in MINITAB to check if data are approximately normally distributed. (b) Use MINITAB to construct a 90% confidence interval for the population mean score and interpret your result. (c) Use MINITAB to construct a 95% confidence interval for the population mean scores and interpret your result. (d) Compare part (b) and (c) and explain which confidence interval is narrower and why?

Answer 1

a ) The probability plot is given below :

Since almost all the data points lie mostly on a straight line , hence we can conclude based on this graph that the data follows approximately normal distribution .

b ) The 90 % confidence interval for the population mean is :

where ,

Required confidence interval :

We are 90 % confident that the value of the population mean will lie in the interval given by

c )  The 95 % confidence interval for the population mean is :

where ,

Required confidence interval :

We are 95 % confident that the value of the population mean will lie in the interval given by  

d ) After comparing parts ( b ) and ( c ) , we conclude that the confidence interval obtained in part ( b ) is narrower than the confidence interval obtained in part ( c ) . A confidence interval for a prescribed level of confidence ( less than 100 % ) implies a range for which we are that confident that the value of the population parameter will lie within that range . Thus the larger the confidence , the wider the interval is . The more sure we are of the confidence interval , the less precise it is. Hence 95 % has a wider confidence interval in comparison to 90 % confidence interval .