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.

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:

100

0.01p

100

0.01

x

p

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 HypothesisClaim about a population characteristic that is

initially assumed to be true. It’s accepted until proven otherwise. It represents no change

Alternative HypothesisCompeting claim – represents changeHas the burden of proof

oH

AH

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.

: 70

: 70o

A

H

H

Implied in this statement is

70

Format

:

: , ,o

A

H parameter hypothesized value

H parameter hypothesized value

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 ErrorReject the Ho and it was really true

Type II ErrorFail to reject the Ho and you should have.

Type I ErrorResult:

Type II ErrorResult:

: Innocent

: Not Innocento

A

H

H

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)