Question

Consider a normal population with an unknown population standard deviation. A random sample results in x− = 47.50 and s2 = 27.04. a. Compute the 90% confidence interval for μ if x− and s2 were obtained from a sample of 15 observations. (Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.) b. Compute the 90% confidence interval for μ if x− and s2 were obtained from a sample of 23 observations. (Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Answer 1

a)

t critical value at 0.10 level with 14 df = 1.761

90% confidence interval for is

- t * S / sqrt(n) <   < + t * S / sqrt(n)

47.5 - 1.761 * sqrt (27.04) / sqrt(15) < < 47.5 + 1.761 * sqrt (27.04) / sqrt(15)

45.14 < < 49.86

905 CI is (45.14 , 49.86)

b)

t critical value at 0.10 level with 22 df = 1.717

90% confidence interval for is

- t * S / sqrt(n) <   < + t * S / sqrt(n)

47.5 - 1.717 * sqrt (27.04) / sqrt(23) < < 47.5 + 1.717 * sqrt (27.04) / sqrt(23)

45.64 < < 49.36

90% CI is (45.64 , 49.36)