Warm Up – Need Clickers and Green Book

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Warm Up – Need Clickers and Green Book. If H 0 : p = 0.6 a what is the standard deviation ? If the standard deviation is 0.03 and H 0 : p = 0.92 what is the p-value if your Use back cover of green book and round percent to a whole number

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### Warm Up – Need Clickers and Green Book

If H0: p = 0.6 awhat is the standard deviation?

If the standard deviation is 0.03 and H0: p = 0.92 what is the p-value if your Use back cover of green book and round percent to a whole number

If the standard deviation is 0.1 and H0: p = 0.6 what is the p-value if your round percent to a whole number

How do you find the p-value?

P-value

the probability that could occur if Ho was correct

1. Find

2. Find standard deviation: use p from H0

3. Find the z-value: use standard dev. from H0

4. Find P-value:use z and look up

on the z-table

Interpreting the p-value…

Overwhelming Evidence

(Highly Significant)

Strong Evidence

(Significant)

Weak Evidence

(Not Significant)

No Evidence

(Not Significant)

0 .01 .05 .10

When do you reject Ho?

Significance Level

Choose the significance level =

reject Ho if P

confidence level is 95%

reject Ho if P

confidence level is 99%

P : then reject Ho

Reject H0

Fail to reject H0

Signficance Level

()

Critical region

Rejection Region for different HA

a

Level of significance =

a

a

/2

/2

HA: μ≠

Two-tail test

0

a

HA: μ >

0

Upper-tail test

a

HA: μ <

Lower-tail test

0

State Hypothesis (H0 & HA)

• Check conditions
• Data: p-hat, stdev, n
• Analysis: Find P-value & draw normal curve
• Conclusion: Reject H0 if P-value is small (statistically significant)

Hypothesis Test:

Does the person who is older win more plays at war than the younger person?

Classwork

green book page 521 #24-27

Complete for homework

Critical Region:
• ISet of all values of the test statistic that would cause a rejection of the

null hypothesis

Significance level:

Critical

Region

### Components of aFormal Hypothesis Test

Critical Region
• Set of all values of the test statistic that would cause a rejection of the
• null hypothesis

Critical

Region

Critical Region
• Set of all values of the test statistic that would cause a rejection of the

null hypothesis

Critical

Regions

Definition

CriticalValue:

is the value (s) that separates the critical region from the values that would not lead to a rejection of H0

Critical Value

Value (s) that separates the critical region from the values that would not lead to a rejection of H0

Critical Value

( z score )

Critical Value

Value (s) that separates the critical region from the values that would not lead to a rejection of H0

Reject H0

Fail to reject H0

Critical Value

( z score )

Controlling Type I and Type II Errors
• a, ß, and n are related
• when two of the three are chosen, the third is determined
• a and n are usually chosen
• try to use the largest a you can tolerate
• if Type I error is serious, select a smaller a value and a larger n value
Conclusions in Hypothesis Testing
• always test the null hypothesis

1. Fail to reject the H0

2. Reject the H0

• need to formulate correct wording of finalconclusion

### Warm up

What do all of these phrases have in common:

The finding is significant at the 0.05 level.

The confidence level is 95 percent.

The Type I error rate is 0.05.

The alpha level is 0.05.

α = 0.05.

There is a 1 in 20 chance of obtaining this result (or one more extreme).

The area of the region of rejection is 0.05.

The p-value is 0.05.

p = 0.05.

FIGURE 7-2 Wording of Conclusions in Hypothesis Tests

Original

claim is H0

(This is the

only case in

which the

original claim

is rejected).

“There is sufficient

evidence to warrant

rejection of the claim

that. . . (original claim).”

Yes

(Reject H0)

Do

you reject

H0?.

No

(Fail to

reject H0)

“There is not sufficient

evidence to warrant

rejection of the claim

that. . . (original claim).”

Original

claim is H1

(This is the

only case in

which the

original claim

is supported).

Yes

(Reject H0)

“The sample data

supports the claim that

. . . (original claim).”

Do

you reject

H0?

No

(Fail to

reject H0)

“There is not sufficient

evidence to support

the claim that. . .

(original claim).”

Type I Error
• The mistake of rejecting the null hypothesis when it is true.
• The probability of doing this is called the significance level, denoted by a(alpha).
• Common choices for a: 0.05 and 0.01
• Example: rejecting a perfectly good parachute and refusing to jump
Type II Error
• the mistake of failing to reject the null hypothesis when it is false.
• denoted by ß (beta)
• Example: failing to reject a defective parachute and jumping out of a plane with it.
Table 7-2 Type I and Type II Errors

True State of Nature

The null

hypothesis is

false

The null

hypothesis is

true

We decide to

reject the

null hypothesis

Type I error

(rejecting a true

null hypothesis)

Correct

decision

Decision

We fail to

reject the

null hypothesis

Type II error

(failing to reject

a false null

hypothesis)

Correct

decision