Question

The employees of Electronics Inc. would like to have a dental plan as part of their benefits package. The question is: How much does a typical employee and his or her family spend per year on dental expenses? A sample of 56 employees reveals the mean amount spent last year was $1850, with a standard deviation of $700.

a. Construct a 90% confidence interval for the population mean. (Round the final answers to the nearest whole dollar.)

Population mean $  $

b. The information from part (a) was given to the president of Electronics Inc. He indicated he could afford $1730 of dental expenses per employee. Is it possible that the population mean could be $1730?

(Click to select)  Yes.  No.  The population mean  (Click to select)  could be  could not be  $1730 because it is  (Click to select)  in the  not in the  interval constructed above.

Answer 1

a)
sample mean, xbar = 1850
sample standard deviation, s = 700
sample size, n = 56
degrees of freedom, df = n - 1 = 55

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.673

ME = tc * s/sqrt(n)
ME = 1.673 * 700/sqrt(56)
ME = 156.4948

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (1850 - 1.673 * 700/sqrt(56) , 1850 + 1.673 * 700/sqrt(56))
CI = (1694 , 2006)

b)

No. The population mean could not be $1730 because it is in the interval constructed above.