Find the mean number of points for the basketball team and the standard deviation.

Player Points St. Dev.

John 5 1

Tim 8 2

Ed 12 4

Marcus 10 3

Demetrius 14 4

Inference Test of Difference of Means

Section 11.1

Experiment

Separate – boys & girls.

Take Pulse rates

Remember….

Independent Selection of one sample does not influence

the selection of the other sample

So if we want to estimate the difference in means between two populations…..

The point estimate is:

So

For the difference of means what is the standard deviation?

The properties of the sampling distribution of

If n1 and n2 are sufficiently large or the populations normal, then the distribution will be approximately normal.

1 2x x

1 2x x 1 2

1 2x x

2 21 2

1 2n n

So what is the z-score for the difference in boys and girls pulse rates?

Remember: Use t test if σ is unknown

T-Test statistic 1 2 1 2

2 21 2

1 2

x xt

s s

n n

Use boxplot to check for normal if samples are small & data given.

So is there a difference between boys and girls?

Assumptions:

D.F. is a little more complicated!

22 21 2

1 22 22 2

1 2

1 2

1 21 1

s sn n

dfs sn n

n n

A conservative estimate of the P-value can be found by using a df = smaller of either n1-1 or n2-1.

Let’s try one!

College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this by asking a random sample of 1296 students who had summer jobs how much they earned. They were then separated into two groups based on gender. Is there a difference in the amount males and females earn?

Amounts different for males & females?

  n mean st. dev.

Males 675 $1884.52 $1368.37

Females 621 $1360.39 $1037.46

Parameter:

= true mean amount males earned

= true mean amount females earned

1

2

Hypothesis

or

Assumptions

1. Random: samples chosen randomly

2. Approximately normal: n1>30 and n2>30.

3. Independent: more than 6750 males and 6210 females

Name

Use a 2 sample T test of means since σ is unknown

Test Statistic

Obtain a P-value

P-value = tcdf (7.81, ∞., 620)*2 ≈ 0

Now to finish it up!

Make a decision

State a conclusion

Reject the Ho since p-value(0) < α (0.05)

There’s sufficient evidence to support the claim that there is a difference in the amounts earned by males and females.

Pooling the Data

If you prove the standard deviations are equal then you can pool the data together.

You don’t want to do this….it’s another type of hypothesis test to prove standard deviations equal

Never Pool!

The Formula Sheet

If you bought a used camera in good condition from a friend, would you pay the same as you would if you bought the same item from a stranger.

Friend Stranger

275 260

300 250

260 175

300 130

255 200

275 225

290 240

300  

Don’t forget the boxplot to show normal!

Homework

Worksheet #1