Question

In: Statistics and Probability

A simple random sample of 60 items resulted in a sample mean of 63. The population...

A simple random sample of 60 items resulted in a sample mean of 63. The population standard deviation is 15.

a. Compute the 95% confidence interval for the population mean (to 1 decimal).

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).

Solutions

Expert Solution

a) Sample size, n = 60

Sample mean, = 63

Standard deviation, = 15

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

At 95% confidence interval estimate of the population mean is,

- E < < + E

which is the required 95% confidence interval for population mean.


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