Question

For these two questions 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 and the sample standard deviation is 5.0 calls per month.

Assume that the population standard deviation is unknown. Find the error of estimate for a 90% confidence interval. Group of answer choices 1.39 1.08 1.43 1.10

Assume that the population standard deviation is unknown. What is the upper bound for a 95% confidence interval? Group of answer choices 43.4 44.2 40.3 43.7

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 42.0

sample standard deviation = s = 5.0

sample size = n = 35

Degrees of freedom = df = n - 1 = 35 - 1 = 34

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,34  = 1.691

Margin of error = E = t/2,df * (s /n)

= 1.691 * ( 5.0/ 35)

Margin of error = E = 1.43

The 90% upper confidence interval estimate of the population mean is,

+ E  

= 42.0 + 1.4 = 43.4

upper bound = 43.4