Question

You intend to estimate a population mean μ from the following sample.

41.7	43.7	37.2	30.5
34.1	21.4	41.5	40
28.4	14.4	35.2	30
42.3	40.1	41	24.2
24.5	47.9	18.9	35.1
34.7	32.9	31.8	43.9
35.9	18.5	22.9	50
42.9	27.2	26.8	28.2
26.6	32.3	29.2	20.7
44.3	37.3	35.6	20.2
19.9	34.9	25.1	30.2

Find the 95% confidence interval. Enter your answer as a tri-linear inequality accurate to two decimal place (because the sample data are reported accurate to one decimal place).

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

sample size ( n ) = 44, c=95%

now calculate sample mean( ) ans sample standard deviation (s) for given data

we get

sample mean( ) = 32.3659

sample standard deviation (s) = 8.7678

formula for confidence interval is

here tc is the t critical value for c=95% with df= n-1 = 44-1= 43

using t table we get

tc = 2.017

32.3659 − 2.666 < <   32.3659 + 2.666

29.70   < <   35.03