### Oct. 2, 2008

## ERROR

reality | |||

Hnull = TRUE | Hnull = False | ||

Decision | reject Hnull | type I (alpha) | correct (1 - beta) |

fail to reject | (1 - alpha)correct | type II (beta) | |

**NOTE: if you increase your probability of making type 1 you decrease making type2 and vice versa, but it is not a linear realitionship.**

**NOTE: significance rate should probably be better than one in twenty or .95.**

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> football<-read.table("Football.dat",header=T)

> attach(football)

**NOTE:Comment the new code for each lab.**

**NOTE: At thirty the sampling distribution tends to become normal, but not always.**

## ERROR

See table and notes above.

## What is the effect and is it useful?

**NOTE: APA says that you must include an effect size.**

>

## Estimates

Error: unexpected '<' in "<"

## Estimates

Point estimate: best one number guess. So guessing the population mean would mean we would guess the sample mean.

> mean(WGR)

[1] 59.16

> mean(BGR)

[1] 44.04

>

**NOTE: remeber the t-test is about making sure that the populations are different in the way wer see the samples to be different.**

Error: unexpected '<' in "<"

**NOTE: remeber the t-test is about making sure that the populations are different in the way wer see the samples to be different.**

> Interval estimate: an interval were we are "pretty sure" that the population characteristic lies.

Error: unexpected symbol in "Interval estimate"

Interval estimate: an interval were we are "pretty sure" that the population characteristic lies.

-we want to make it useful and we want to be confident in it. Sampling error and degree of cinfidence affects the width of the interval.

Point estimate - error and point estimate + error make up the bounds of our interval.

point est. - error <= parameter <= point est. + error

P(-1.96 <= Zscore <= 1.96) = .95

Zscore is observation minus mean divided by the standard deviation of the destributionP(-1.96

P(-1.96 <= Z <= 1.96) = .95

P((mu-hat-1.96(sigma-hat/root-n))<=mu<=(mu-hat+1.96(sigma-hat/root-n))=.95

mu-hat=59.16

sigma-hat=13.92

n=50

> sd(WGR)

[1] 13.92305

> err<-1.96*sd(WGR)/sqrt(50)

> mean(wgr)-err

Error in mean(wgr) : object "wgr" not found

> mean(WGR)-err

[1] 55.30073

> mean(WGR)+err

[1] 63.01927

our .95 confidence interval is therefore 55.50 - 63.02

> t.test(WGR, mu=76,alt="two.sided")

One Sample t-test

data: WGR

t = -8.5525, df = 49, p-value = 2.766e-11

alternative hypothesis: true mean is not equal to 76

95 percent confidence interval:

55.20311 63.11689

sample estimates:

mean of x

59.16

See above "95 percent confidence interval"

> t.test(WGR,mu=76,alt="two.sided",conf.level=.99)

One Sample t-test

data: WGR

t = -8.5525, df = 49, p-value = 2.766e-11

alternative hypothesis: true mean is not equal to 76

99 percent confidence interval:

53.88313 64.43687

sample estimates:

mean of x

59.16

Our .01 or 99 percent confidence interval is 53.88 to 64.44

When you give an interval estimate you are either right or wrong. In reality there is not 95% sure. It either is or isn't

Confidence intervals only work for two sided tests. For a one-sided test you have to compute an asymetric confidence interval.

> help(t.test)

If one did a one-sided test, one would not provide this type of effect size.

>