10.1 Statistics

Question

Suppose you administer a certain aptitude test to a random sample of 9 students in your school, and that the average score is 105. We want to determine the mean μ of the population of all students in the school. Assume a standard deviation of σ = 15 for the test.

Explain the meaning of “98% confident.” Don’t just use synonyms for “confident”.

Answer 1

I am interpreting your question as indicating you want to determine a 98% confidence interval for the mean.

That would be sample mean +/- z-critical * standard deviation/square root(sample size)

where sample mean is 105, z-critical for 98% confidence level is 2.33, standard deviation is 9 and sample size is 3.

plug values into formula to get confidence interval.

98% confident mean that i98% percent of the samples will have 98% confidence intervals that contain the true population mean.