Question

Assuming that the population is normally​ distributed, construct a 99% confidence interval for the population​ mean, based on the following sample size of n=7.​

1, 2,​ 3,4, 5, 6​,and 30  

Change the number 30 to 7 and recalculate the confidence interval. Using these​ results, describe the effect of an outlier​ (that is, an extreme​ value) on the confidence interval.

Find a 99 % confidence interval for the population mean.

​(Round to two decimal places as​ needed.)

Change the number 30 to 7. Find a 99 % confidence interval for the population mean.

nothingless than or equals≤muμless than or equals≤nothing

​(Round to two decimal places as​ needed.)

What is the effect of an outlier on the confidence​ interval?

A.The presence of an outlier in the original data decreases the value of the sample mean and greatly decreases the sample standard​ deviation, narrowing the confidence interval.

B.The presence of an outlier in the original data increases the value of the sample mean and greatly inflates the sample standard​ deviation, widening the confidence interval.

C.The presence of an outlier in the original data decreases the value of the sample mean and greatly inflates the sample standard​ deviation, widening the confidence interval.

D.The presence of an outlier in the original data increases the value of the sample mean and greatly decreases the sample standard​ deviation, narrowing the confidence interval.

Answer 1

Sample Mean,    x̅ = Σx/n = 7.286

Sample Size ,   n =    7

sample std dev ,    s =    10.1606

degree of freedom=   DF=n-1=   6  
't value='   tα/2=   3.7074   [Excel formula =t.inv(α/2,df) ]
          
Standard Error , SE =   s/√n =   3.8404  
margin of error ,   E=t*SE =   14.238  

confidence interval is           
Interval Lower Limit=   x̅ - E =    -6.95   
Interval Upper Limit=   x̅ + E =    21.52

-----------------------------------------------------------------------------------

sample std dev ,    s =    2.1602
Sample Size ,   n =    7
Sample Mean,    x̅ =   4.000

Level of Significance ,    α =    0.01

degree of freedom=   DF=n-1=   6  
't value='   tα/2=   3.7074   [Excel formula =t.inv(α/2,df) ]
          
Standard Error , SE =   s/√n =   0.8165  
margin of error ,   E=t*SE =   3.027  

confidence interval is           
Interval Lower Limit=   x̅ - E =    0.97
Interval Upper Limit=   x̅ + E =    7.03

---------------------------------------

effect of an outlier on the confidence​ interval

The presence of an outlier in the original data increases the value of the sample mean and greatly inflates the sample standard​ deviation, widening the confidence interval