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Hypothesis Tests & Procedures & Errors

ericnichols
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Hypothesis Tests & Procedures & Errors

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  1. A study of the career paths of hotel general managers sent questionnaires to a SRS of hotels. The average time these 114 general managers had spent with their current company was 11.78. Construct & interpret a 98% confidence interval for the mean number of years spent with their company if the standard deviation is known to be 3.2 years.A company found that of the 84 applicants whose credentials were checked, 15 lied about having a degree. Calculate a 90% confidence interval for the true proportion of applicants who lie about having a degree.

  2. A study of the career paths of hotel general managers sent questionnaires to a SRS of hotels. The average time these 114 general managers had spent with their current company was 11.78. Construct & interpret a 98% confidence interval for the mean number of years spent with their company if the standard deviation is known to be 3.2 years.

  3. A company found that of the 84 applicants whose credentials were checked, 15 lied about having a degree. Calculate a 90% confidence interval for the true proportion of applicants who lie about having a degree.

  4. Hypothesis Tests & Procedures & Errors Section 9.1

  5. Confidence & Significance Tests • Confidence Interval • Goal is to estimate a population parameter • Significance Test (Hypothesis Test) • Goal is to assess the evidence provided by data about some claim concerning a population.

  6. Card Activity • Guess the proportion of red cards • Draw cards and make an estimate of the proportion of red cards. • Do you want to make an alternate guess?

  7. Hypothesis • It’s a statement about the value of a population’s characteristic. • Possible hypothesis: • Not Possible:

  8. Test Procedure – Test of Hypothesis • It’s a method for using sample data to decide between 2 competing claims about a characteristic of a population such as a mean or a proportion.

  9. Two Claims • Null Hypothesis • Claim about a population characteristic that is initially assumed to be true. • It’s accepted until proven otherwise. • It represents no change • Alternative Hypothesis • Competing claim – represents change • Has the burden of proof

  10. Paramedics need to respond to accidents as quickly as possible – they need medical attention within 8 minutes of the crash. One city found that their response time last year was 6.7 minutes with st. dev of 2 minutes. This year, they selected a SRS of 400 calls and found the response time was 6.48 minutes. Do these data provide good evidence that response times have decreased since last year?

  11. Example • Nutritionists claim the average number of calories in a serving of popcorn is 70. You suspect it is higher. Implied in this statement is

  12. Format

  13. Example • Machine is calibrated to achieve design specification of 3 inches – diameter of a tennis ball. We are concerned that it is no longer the case.

  14. Example • The company who makes M&M’s says that 30% of the M&M’s that they produce are green. You suspect that it is less than that.

  15. Hypothesis Test • It’s only capable of showing strong support for the Alternate Hypothesis by rejecting the Null Hypothesis. • When the Null is not rejected we simply say that we failed to reject the Null. It doesn’t mean that it’s accepted – only that we’re unable to prove otherwise.

  16. Just as a jury may reach a wrong decision, testing Hypothesis with sample data may lead us to the wrong conclusion

  17. Error – Risk of error is the price researchers pay for basing inference on a sample. • Type I Error • Reject the Ho and it was really true • Type II Error • Fail to reject the Ho and you should have.

  18. Type I Error • Result: • Type II Error • Result:

  19. U.S. Dept. of Transportation reported that 77% of domestic flights were “on time.” The Airline company offers a bonus if their ontime flights exceeds the 77%. • Hypothesis • Type I Error • Type II Error

  20. Salmonella contamination for chicken is 20%. If the salmonella rate is more, the chicken is rejected because it can make people extremely sick. • Hypothesis • Type I Error • Type II Error

  21. Level of Significance • It’s the probability of a Type I error • We use the symbol – • Type II error is represented as

  22. Using of 0.01, 0.05, 0.10 • If Type I error is worse, then you want to lower it’s chance of occurring – so use a smaller • If Type II error is worse, then you want to increase possibility of Type I – so use a larger

  23. Homework • Page 546 (1-10) odd, (19-21) odd (27, 29)

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