In: Statistics and Probability
In order to estimate the number of calls to expect at a new suicide hotline, volunteers contact a random sample of 50 similar hotlines across the nation and find that the sample mean is 32.0 calls per month. Construct a 99% confidence interval for the mean number of calls per month. Assume that the population standard deviation is known to be 9.5 call per month.
(Please show all work)
Solution :
Given that,
Point estimate = sample mean =
= 32
Population standard deviation =
= 9.5
Sample size = n =50
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576 ( Using z table )
Margin of error = E = Z/2* ( /n)
= 2.576 * (9.5 / 50)
= 3.46
At 99% confidence interval mean is,
- E < < + E
32-3.46 < < 32+3.46
28.54< < 35.46
(28.54 , 35.46)