Question

-A random sample of 15 checking accounts at a bank showed an average balance of $280. The standard deviation of the sample was $60. Construct a 90% confidence interval for the mean and explain what it shows you in the context of the problem. Show your work and show your calcualtor steps.

-A local health center noted that in a sample of 400 patients 80 were referred to them by the local hospital. Provide a 95% confidence interval for the percentage of patients who were referred to the health center by the hospital and explain what it means in the context of the problem. Show your work and show your calcualtor steps.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 280

sample standard deviation = s = 60

sample size = n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,14 = 1.761

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

= 1.761 * ( 60 / 15)

= 27.3

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

- E < < + E

280 - 27.3 < < 280 + 27.3

252.7 < < 307.3

(252.7 , 307.3)