What is the margin of error for the sample mean at a 95% confidence level? Hint: Look at the notes given above to see how the margin of error is computed. 2. Will the margin of error increase/decrease if 200 delinquent credit cards were sampled instead of 100? Why? Hint: Look at the notes given above to see how the margin of error is computed and how the sample size n impacts its value. 3. Give a 95% confidence interval for the mean amount owed on all delinquent credit card accounts for this bank (i.e. population mean µ). Hint: Look at the notes given above to see how the confidence interval for the population mean is computed.
A bank took a sample of 100 of its delinquent credit card accounts and found that the mean owed on these accounts was $2,130. It is known that the standard deviation for all delinquent credit card accounts at this bank is $578.
(Hint: First write out the values for n, x¯, and σ)
1. What is the margin of error for the sample mean at a 95% confidence level? Hint: Look at the notes given above to see how the margin of error is computed.
2. Will the margin of error increase/decrease if 200 delinquent credit cards were sampled instead of 100? Why? Hint: Look at the notes given above to see how the margin of error is computed and how the sample size n impacts its value.
3. Give a 95% confidence interval for the mean amount owed on all delinquent credit card accounts for this bank (i.e. population mean µ). Hint: Look at the notes given above to see how the confidence interval for the population mean is computed.
4. Will the confidence interval become wider or narrower if 200 delinquent credit cards were sampled instead of 100? Why? Hint: Look at the notes given above to see how the confidence interval is computed and how the sample size n impacts its lower and upper bounds and hence the width.
5. Will the confidence interval become wider or narrower if the sample size is still 100 but the confidence level is increased from 95% to 99%? Why?
Hint: Look at the notes given above to see how the confidence interval is computed and how the multiplier depends on confidence level i.e. z∗ impacts its lower and upper bounds and hence the width.
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