Question

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

Answer 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)