Question

2) In order to estimate the number of calls to expect at a new suicide hotline, volunteers contact a random sample of 35 similar hotlines across the nation and find that the sample mean is 42.0 calls per month.

a. Construct a 95% confidence interval for the mean number of calls per month. Assume that the population standard deviation is known to be 6.5 calls per month.

b. Interpret the construction done in part “a”.

Answer 1

a)

We have given that,              
              
Sample mean =42   calls per month.  
Population standard deviation=6.5 calls per month.  
Sample size=35      
Level of significance =1-0.95=0.05      
Z critical value (by using Z table)=1.96      
              

b) We are 95% confident that the population mean number of calls per month is between 39.85 to 44.15