Question

3. In order to approximate the number of text messages sent daily by Swedish teenagers, Neu Star Communications took a random sample of Swedish youth, finding the number of text messages they sent on a given day in 2018:

HOURS

78	86	86	79	84	79	89	86	86	84	79	81

1. What is the point estimate of the population mean? (Round your answer to 2 decimal places.)

ESTIMATED POPULATION MEAN: …..............?

2. Develop a 98% confidence interval for the population mean. (In your calculations, use 2 decimal places for the mean and 3 decimal places for other values. Round your final answers to 2 decimal places.)

CONFIDENCE INTERVAL FOR THE POPULATION MEAN:…........... AND …............?

Answer 1

a) estimated population mean =  x̅ = ΣX/n =    83.08

b)

Level of Significance ,    α =    0.02          
degree of freedom=   DF=n-1=   11          
't value='   tα/2=   2.718   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   3.704/√12=   1.0693          
margin of error , E=t*SE =   2.7181   *   1.0693   =   2.9063
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    83.08   -   2.9063   =   80.1737
Interval Upper Limit = x̅ + E =    83.08   -   2.9063   =   85.9863
98%   confidence interval is (   80.17 < µ <   85.99 )