Question

# A simple random sample of size n is drawn from a population that is normally distributed....

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found to be 105​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct a 90​% confidence interval about mu if the sample​ size, n, is 24. ​(b) Construct a 90​% confidence interval about mu if the sample​ size, n, is 20. ​(c) Construct an 80​% confidence interval about mu if the sample​ size, n, is 24. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed? LOADING... Click the icon to view the table of areas under the​ t-distribution. ​(a) Construct a 90​% confidence interval about mu if the sample​ size, n, is 24. Lower​ bound: nothing​; Upper​ bound: nothing ​(Use ascending order. Round to one decimal place as​ needed.)

a)

 sample mean 'x̄= 105 sample size   n= 24 sample std deviation s= 10 std error 'sx=s/√n= 2.0412
 for 90% CI; and 23 df, value of t= 1.714 margin of error E=t*std error    = 3.50 lower bound=sample mean-E = 101.50 Upper bound=sample mean+E = 108.50 from above 90% confidence interval for population mean =(101.5, 108.5 )

b)

90% confidence interval for population mean =(101.1 , 108.9 )

c)

80% confidence interval for population mean =(102.3 , 107.7 )

d)

No since sample size is less than 30 , we Could not have computed the confidence intervals

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