Question

73. A survey asked couples for the number of years they had known each other before their divorce. A preliminary random sample of 46 couples had a standard deviation of 4.346 years. How large a sample is needed to construct a 90 percent confidence interval for the mean time each couple knew each other before the divorce if the estimate is to be within .5 year of the actual time? 74. Using the data in problem 73, how large a sample is needed to construct a 95 percent confidence interval for the mean time each couple knew each other before the divorce if the estimate is to be within .5 year of the actual time?

The answer for number 74 plz.

Answer 1

74)

Standard Deviation ,   σ =    4.346                  
sampling error ,    E =   0.5                  
Confidence Level ,   CL=   95%                  
                          
alpha =   1-CL =   5%                  
Z value =    Zα/2 =    1.960   [excel formula =normsinv(α/2)]              
                          
Sample Size,n = (Z * σ / E )² = (   1.960   *   4.346   /   0.5   ) ² =   290.226
                          
                          
So,Sample Size needed=       291