Question

In: Statistics and Probability

In order to estimate the number of calls to expect at a new suicide hotline, volunteers...

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)

Solutions

Expert Solution

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)

orchestra answered 3 years ago
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