Question

# A college admissions director wishes to estimate the mean age of all students currently enrolled. The...

A college admissions director wishes to estimate the mean age of all students currently enrolled. The age of a random sample of 23 students is given below. Assume the ages are approximately normally distributed. Use Excel to construct a 90% confidence interval for the population mean age. Round your answers to two decimal places and use increasing order.

Age
25.8
22.2
22.5
22.8
24.6
24.0
22.6
23.6
22.8
23.1
21.5
21.4
22.5
24.5
21.5
22.5
20.5
23.0
25.1
25.2
23.8
21.8
24.1

 Age(x) (x-xbar)^2 25.8 7.266541 22.2 0.817845 22.5 0.365236 22.8 0.092628 24.6 2.236975 24 0.802193 22.6 0.254367 23.6 0.245671 22.8 0.092628 23.1 1.89E-05 21.5 2.573932 21.4 2.904802 22.5 0.365236 24.5 1.947845 21.5 2.573932 22.5 0.365236 20.5 6.782628 23 0.010888 25.1 3.982628 25.2 4.391758 23.8 0.483932 21.8 1.701323 24.1 0.991323 sum 531.4 41.24957 mean 23.10435

s=sample standard deviation

s=1.3693

#90% confidence interval for the population mean age

n=23    s=1.369

90 % confidence interval forPOPulation Mean is

ME=margin of error

t=critical value

t=

t​​​​22,0.05=1.7171

ME=0.4901

​​​

t is obtained from t- table with corresponding degree of freedom (n-1) is22

# using Excell =TINV(0.1,22)

90 % Confidence interval for Population Mean is

(23.10-0.4901,23.10+0.4901)

(22.61,23.59)

#90% confidence interval for the population mean age. is (22.61,23.59)

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