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 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.

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 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.

Hypothesis Tests & Procedures & Errors Section 9.1

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.

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?

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

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.

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

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?

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

Format

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.

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.

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.

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

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

Type I Error  Result: Type II Error  Result:

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

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

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

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

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