Transcript Notes on Types of Errors and Writing Hypotheses

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

 p  0.01
 x  100

 p  0.01
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  Ho 
 Claim
about a population characteristic that is
initially assumed to be true.
 It’s accepted until proven otherwise.
 It represents no change

Alternative Hypothesis  H A 
claim – represents change
 Has the burden of proof
 Competing

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.
 H o :   70

 H A :   70
Implied in this statement is
  70
Format
 H o : parameter  hypothesized value

 H A : 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 Error
 Reject

the Ho and it was really true
Type II Error
 Fail
to reject the Ho and you should have.
 H o : Innocent

 H A : 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
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)