MATH 533 Week 4 Discussion: Confidence Intervals in Business

MATH 533 Week 4 Discussion: Confidence Intervals in Business Consider when businesses might use confidence intervals to estimate values, such as in sales projections, marketing results, and so forth. Describe a business decision that could be helped with confidence intervals. Then create a problem with numbers from which another student could calculate a confidence interval and make a decision. Professor and class, A group of 10 foot surgery patients had a mean weight of 240 pounds. The sample standard deviation was 25 pounds. Find a confidence interval for a sample for the true mean weight of all foot surgery patients. Find a 95% CI. Confidence Interval For a Sample: Steps Question: Step 1: Subtract 1 from your sample size. 10 – 1 = 9. This gives you degrees of freedom, which you’ll need in step 3. Step 2: Subtract the confidence level from 1, then divide by two. (1 – .95) / 2 = .025 Step 3: Look up your answers to step 1 and 2 in the t-distribution table. For 9 degrees of freedom (df) and α = 0.025, my result is 2.262. df α = 0.1 0.05 0.025 0.01 0.005 0.001 0.0005 ∞ tα=1.282 1.645 1.960 2.326 2.576 3.091 3.291 1 3.078 6.314 12.706 31.821 63.656 318.289 636.578 2 1.886 2.920 4.303 6.965 9.925 22.328 31.600 3 1.638 2.353 3.182 4.541 5.841 10.214 12.924 4 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 1.476 2.015 2.571 3.365 4.032 5.894 6.869 6 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 1.397 1.860 2.306 2.896 3.355 4.501 5.041 9 1.383 1.833 2.262 Step 4: Divide your sample standard deviation by the square root of your sample size. 25 / √(10) = 7. Step 5: Multiply step 3 by step 4. 2.262 × 7. = 17.8826802 Step 6: For the lower end of the range, subtract step 5 from the sample mean. 240 – 17.8826802 = 222.117 Step 7: For the upper end of the range, add step 5 to the sample mean. 240 + 17.8826802 = 257.883 That’s how to find the confidence interval for a sample! Like the explanation on how to find a confidence interval? Check out our statistics how- to book, with a how-to for every elementary statistics problem type. .