Question

You intend to estimate a population mean μ from the following sample.

73.1	61.9	55.1	116.3
55.3	69.2	91.2	70.3
74	50.1	71.7	58.8
117.1	50.6	43.3	82.6
80.7	60.1	67.4	70.3
70.2	66.4	46.7	115.2
58.9	92.5	65.9	81.7
59.1	90.6	56.9	55.8
74.9	65.7	113	58.7
87.8	73.7	89.2	58.3
86.8	79.5	69.8	52.3
72.9	81.5	55	52.7
56.1	37.6	49.9	57.3
94.5	58.8	79.5	85.4
105.5

Find the 99% confidence interval. Enter your answer as a tri-linear inequality accurate to two decimal place (because the sample data are reported accurate to one decimal place).

_______ < μ < _______

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

We have for given data,          
          
Sample mean =71.4982  
Sample standard deviation =18.8184
Sample size =57  
Level of significance=   1-0.99=   0.01  
Degree of freedom =n-1=57-1=56  
          
t critical value is (by using t table)=   2.667
          
Confidence interval formula is   

=(64.852,78.145)
      
          
          
          
Lower confidence limit=   64.852  
          
Upper confidence limit=   78.145  

64.852< μ < 78.145