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.

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.

 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.

 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?


It’s a statement about the value of a population’s characteristic.
  
100
 Possible hypothesis: 0.01
 Not Possible:
 

 p

100
0.01


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.

 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?

 Nutritionists claim the average number of calories in a serving of popcorn is 70. You suspect it is higher.



H
H o
A
:
:



70

70
Implied in this statement is
 
70




H : parameter hypothesized value o

H : parameter
A hypothesized value

 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.


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.


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

 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.




H
H o
A
: Innocent
: Not Innocent
 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


It’s the probability of a Type I error
 We use the symbol –

 Type II error is represented as


 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


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