Examples CI for mean

1
Examples (CI for mean µ)

• Example 1
• A random sample of 100 observations from a
  normally distributed population possesses a mean
  equal to 83.2 and a standard deviation equal to
  6.4.
• a. Find a 95 confidence interval for µ.
• b. What do you mean when you say that a
  confidence coefficient is .95?
• c. Find a 99 confidence interval for µ.
• e. Would your confidence intervals of parts a and
  c be valid if the distribution of the original
  population was not normal?

2

• Example 2.
• A simple random sample of size n4 has a mean
  equal to 85 and a standard deviation equal 7.7.
• a. Find a 95 confidence interval for the
  population mean.
• b. Find a 99 confidence interval for the
  population mean.

3

• Example 3.
• Refer to the chance examination of SAT scores of
  students who pay a private tutor to help them
  improve their results. A survey of 265 students
  who paid a private tutor to help them improve
  their scores is conducted and the result is as
  follows.
• Construct and interpret a 99 confidence
  interval for the population mean change in
  SAT-Math score for students who pay a private
  tutor.