Question

A simple random sample of 40 items resulted in a sample mean of 30. The population standard deviation is o = 15. a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place. b. Assume that the same sample mean was obtained from a sample of 90 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.

Answer 1

a)

95% confidence interval for $\mu$ is

$\bar{x}$ - Z$\alpha$/2 * $\sigma$ / sqrt(n) < $\mu$ < $\bar{x}$ + Z$\alpha$/2 * $\sigma$ / sqrt(n)

30 - 1.96 * 15 / sqrt(40) < $\mu$ < 30 + 1.96 * 15 / sqrt(40)

25.4 < $\mu$ < 34.6

95% CI Is ( 25.4 , 34.6 )

b)

95% confidence interval for $\mu$ is

$\bar{x}$ - Z$\alpha$/2 * $\sigma$ / sqrt(n) < $\mu$ < $\bar{x}$ + Z$\alpha$/2 * $\sigma$ / sqrt(n)

30 - 1.96 * 15 / sqrt(90) < $\mu$ < 30 + 1.96 * 15 / sqrt(90)

26.90 < $\mu$ < 33.10

95% CI Is ( 26.90 , 33.10 )