Question

Data on 43 college graduates show that the mean time required to graduate with a​ bachelor's degree is 5.14 years with a standard deviation of 1.66 years. Use a single value to estimate the mean time required to graduate for all college graduates.​ Also, find the​ 95% confidence interval for the mean time required to graduate for all college graduates. The mean time required to graduate for all college graduates is approximately ? years (round to nearest hundreth as needed) Thus, the​ 95% confidence interval for the mean time required to graduate for all college graduates ranges from ?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 5.14

Population standard deviation = = 1.66

Sample size = n = 43

  At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (1.66 / 43)

= 0.50

At 95% confidence interval estimate of the population mean is,

- E < < + E

5.14 - 0.50 < < 5.14 + 0.50

4.64 < < 5.64

(4.64 , 5.64 )