Conditions for Inference

9.3 Conditions 9.3 CONDITIONS FOR INFERENCE 1. Sample is not biased Check that the sample was an SRS 2. Sample is large enough Number of successes and failures are greater than 10 3. Sample is not too large Population is over ten times the sample size Example 1 2 Parts For the conditions you need two parts: 1. The conditions 2. The check 1. SRS Either SRS or assume representative sample 2. Large Enough np = _____ n(1 - p) = ____ > 10 3. population > 10n Not all samples can be used to create Confidence Intervals or be used for Tests of Significance. Need to check 3 conditions to make sure we can run a test or create an interval: Many people have trouble setting up all the features of their cell phones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 94% of customers succeed. The company tests the new system on 200 people, of whom 184 were successful. Is this strong evidence that the new system fails to meet the company’s goal? Conditions Check 1. SRS Assume sample is representative 2. Large Enough np = 200(.94) = 188 n(1 – p) = 200(.06) = 12 10n = _____ 3. population > 10n > 10 10n = 2000, there are more than 2000 people Example 2 Example 3 • In a rural area, only about 30% of the wells that are drilled • A company with a fleet of 150 cars found that the find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing”—using a forked stick to indicate where the well should be drilled. You check a SRS of 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? Conditions Check emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that more than 20% of the fleet might be out of compliance? Conditions Check 1. SRS Stated SRS 2. Large Enough np = 80(.30) = 24 n(1 – p) = 80(.70) = 56 3. population > 10n 10n = 800, there are more than 800 possible customers > 10 1. SRS Assume sample is representative 2. Large Enough np = 22(.20) = 4.4 n(1 – p) = 22(.80) = 17.6 3. population > 10n 10n = 220, there are only 150 cars < 10 CONDITIONS HAVE NOT BEEN MET! Example 4 Example 5 • A magazine is considering the launch of an online edition. • A company is criticized because only 13 of 43 people in The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacted a simple random sample of 500 current subscribers, and 137 of those surveyed expressed interest. What should the company do? Conditions Check executive-level positions are women. The company explains that although this proportion is lower than it might wish, it’s not surprising given that only 40% of all its employees are women. What do you think? Conditions Check 1. SRS Stated SRS 2. Large Enough np = 500(.25) = 125 n(1 – p) = 500(.75) = 375 3. population > 10n 1. SRS Assume sample is representative 2. Large Enough np = 43(.4) = 17.2 n(1 – p) = 43(.6) = 25.8 > 10 10n = 5000, there are more than 5000 current readers 3. population > 10n > 10 10n = 430, there may not be more than 430 executive-level positions Example 6 Example 7 • A random sample of 540 CB South students found that • A city ballot includes a local initiative that would legalize 528 were carrying a cell phone on them. Create and interpret a 95% confidence interval for the proportion of students carrying a cell phone. Conditions Check gambling. The issue is hotly contested. The local newspaper finds that 53% of 1200 voters that wrote into the newspaper plan to vote “yes.” Create a 90% confidence interval for the proportion of voters that will vote “yes” on the gambling issue. Conditions Check Sample is not representative 1. SRS because of bias sample 1. SRS Stated SRS 2. Large Enough np = 528 n(1 – p) = 12 3. population > 10n 10n = 5400, there are more than 5400 high school students > 10 2. Large Enough np = 1200(.53) = 636 n(1 – p) = 1200(.47) = 564 3. population > 10n 10n = 12000, there are more than 12000 voters > 10 Because of biased sample the conclusions would not be valid!