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# Statistical Calculations Involving Confidence Intervals

James Jackson, owner of James Contracting Company, is worried about shipping costs and admin costs that incur with small purchase orders. So they reduce spending in this area, he created an incentive plan for orders over \$40 so that hey may encourage customers to lower the # of small orders into bigger orders. This is the amount per transaction for a sample of twenty eight customers:

\$10, \$15, \$20, \$25, \$15, \$17, \$41, \$50, \$5, \$9, \$12, \$14, \$35, \$18, \$17, \$28, \$29, \$11, \$11, \$43,\$54, \$7
\$8, \$16, \$13, \$18

a) Given the data above, what is the forecast for the amount of the next customer order?

b) If the policy is successful (by creating this incentive plan), will the standard deviation remain unaffected, increase or decrease? Also, will the mean of the distribution remain unaffected, increase or decrease?

3) From data on a large sample of sales transactions, a small business owner reports that a 95% confidence interval for the mean profit per transaction is (23.41, 102.59). Use these data to determine the following:

What is the point estimate (best guess ) of the mean and its 95% error margin. Also, find a 90% confidence interval for the mean.

Doubts or Drafts: I'm estimating the best guess is 22.4 but I needed clarification on whether this is right. Also, with the 90% confidence interval, what are the steps I'd need to take to solve this? I do know that, to figure out the z score, the formula is Z = X - mean / standard deviation. However, what is the X in this instance?

#### Solution Preview

a) Given the above data, the forecast for the amount of the next customer order is \$20.81 (the mean of the data).

b) If the policy is successful, the standard ...

#### Solution Summary

I posted the answers to some statistics questions involving the standard deviation and 90% confidence interval pertaining to a given set of data.

\$2.19