Question

The following frequency distribution reports the hourly rate for a sample of 70 workers. The population follows the normal distribution.

Hourly rate ($) Frequency 0 but less than or equal to 5 4 5 but less than or equal to 10 15 10 but less than or equal to 15 27 15 but less than or equal to 20 18 20 but less than or equal to 25 6 a) Calculate the sample mean and sample standard deviation for the grouped data. b) Construct a 95% confidence interval for the true mean hourly rate of the workers. Interpret your answer.

Answer 1

sample std dev ,    s =    5.1182
Sample Size ,   n =    70
Sample Mean,    x̅ =   13.0000

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   69          
't value='   tα/2=   1.995   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   5.1182   / √   70   =   0.6117
margin of error , E=t*SE =   1.9949   *   0.6117   =   1.2204
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    13.00   -   1.220392   =   11.7796
Interval Upper Limit = x̅ + E =    13.00   -   1.220392   =   14.2204
95%   confidence interval is (   11.78   < µ <   14.22   )