Question

Find a confidence interval for μ assuming that each sample is from a normal population. (Round the value of t to 3 decimal places and your final answers to 2 decimal places.)

(a) x⎯⎯x¯ = 25, s = 5, n = 7, 90 percent confidence.
  
The 90% confidence interval is  to  

(b)   x⎯⎯x¯ = 50, s = 4, n = 19, 99 percent confidence.
  
The 99% confidence interval is  to  

(c) x⎯⎯x¯ = 121, s = 14, n = 29, 95 percent confidence.
  
The 95% confidence interval is  to

Answer 1

a) = 25, s = 5, n = 7, c = 90%

formula for confidence interval is

Where tc is the t critical value for c= 90 % with df = n-1 = 7-1 = 6

using t table we get critical value as

tc = 1.943

21.328 <    < 28.672

  
The 90% confidence interval is 21.33 to 28.67

(b)   = 50, s = 4, n = 19, c = 99%

formula for confidence interval is

Where tc is the t critical value for c= 99 % with df = n-1 = 19-1 = 18

using t table we get critical value as

tc = 2.878

47.359 <    < 52.641

  
The 99% confidence interval is 47.36 to 52.64

(c) = 121, s = 14, n = 29, c = 95%

formula for confidence interval is

Where tc is the t critical value for c= 95 % with df = n-1 = 29-1 = 28

using t table we get critical value as

tc = 2.048

115.67 <    < 126.33

The 95% confidence interval is 115.67 to 126.33