Question: The mean score on a standardized test is 100 with a standard deviation of 8. A random sample of 48 scores was found to have a mean of 98. Find the 95% confidence interval.
A ) The interval is between 97.75 and 102.25 B ) The interval is between 1.15 and 100 C ) The interval is between 100 and 98 D ) The interval is between 79.75 and 20.25
Steps to derive
1 The 95% confidence interval is between μ - 1.96σe and
μ + 1.96σe, where μ is the population mean and σe is the standard error.
2σe= σn, where σ is the standard deviation of the population and n is the number of elements in the sample
3σe= 848≈ 1.15
4 μ - 1.96σe = 100 - 1.96 (1.15) ≈ 97.75
5 μ + 1.96σe = 100 + 1.96 (1.15) ≈ 102.25
6 The 95% confidence interval is between 97.75 and 102.25.
