I.     t-test

A. Similar to Z test, but use when do not know the population sd (which is most of the time)

B. Same formula, but insert the standard deviation of the sample for the sd of the population

II.  Sampling Distribution of t

A. Definition - probability distribution of t values that would occur if all possible different samples of a fixed size N were drawn from the null-hypothesis population.

1.   

2.   

B. Distribution is normal and looks similar to z distribution if

1.   

2.   

3.  However,

C.Degrees of freedom (df) - the number of scores that are free to vary in calculating that statistic

III.          Comparing t and z distributions

A. As df increase

B. If df = infinity

C.Why?

D.There is more variability in

E. The tails of the t distribution are

F. For a given alpha level, the critical value of t is _____________ than z, making the t-test __________ sensitive than the z test

IV.         Example problem: Meanpop = 13.0, sdpop = ?, sample N = 15, Mean = 11.0 and sd = 3.34

A. What is Ho?

B. What is nondirectional H1?

C.Did it work if alpha = .05 2 tail?

1.  Recall Formula:

2.  Insert Numbers

3.  = -2.32

4.  Compare to table D

V. Alternate Calculation: Appropriate when you have the raw scores, saves you from calculating the sd and reduces rounding errors (this is just an algebraic manipulation)

A. Insert Formula

B. Insert Example

VI.         When is the t-test appropriate

A.  

B.  

C. 

D. 

1.   

2.   

VII.      Confidence Intervals

A. Confidence Interval - Range of values that probably contain the population value

B. Confidence Limits - values that bound the confidence interval

C.95% Confidence interval -

1.  Calculate

2.  Get t

3.  Calculate

4.  Proper statement is that the probability is .95 that the interval contains the population mean. This is because the population mean is constant, but the interval will vary from sample to sample

5.  Can do this for any % confidence interval, just change the t crit

VIII.  Testing the Significance of Pearson's r

A. Test the significance of r obtained

B. Ho =

C.H1 =

D.Generate the Sampling Distribution of r, same as we've been doing

1.   

2.   

E. Can evaluate the significance of r using the t-test

1.  Using an Equation similar to t

2.  Where

a)  Rho = 0 (null hypothesis)

b) Df = N - 2

F. However, It is easier to calculate r crit - Given in table E for different df