One of the characteristics of a credit card is the average outstanding balance. A group of researchers wants to estimate the average outstanding balance using a randomly selected sample of 30 customers. The average monthly balance of the sample is calculated as $2579.12. Construct and interpret a 94% confidence interval for the average outstanding balance assuming that the population standard deviation is $2863.3.
  1. Procedure:
  2. Assumptions: (select everything that applies)
  3. Unknown parameter:
  4. Point estimate: =dollars (Round the answer to 2 decimal places)
  5. Confidence level % and α=\displaystyle \alpha= , also
    •  α2=\displaystyle \frac{\alpha}{{2}}= , and 1α2=\displaystyle {1}-\frac{\alpha}{{2}}=
    • Critical values: (Round the answer to 2 decimal places)
      • left= right=
  6. Margin of error (if applicable): (Round the answer to 2 decimal places)
  7. Lower bound: (Round the answer to 2 decimal places)
  8. Upper bound: (Round the answer to 2 decimal places)
  9. Confidence interval:(, )
  10. Interpretation: We are % confident that the average outstanding balance on a credit card is between dollars and dollars.

Based on the confidence interval, is it reasonable to believe that the average outstanding balance on a credit card is greater than 2300 dollars? Explain.

, because 2300 dollars.