H1H1

Ho

Z = 0

Two Tailed test

Z score where 2.5% of the distribution lies in the tail:

Z = + 1.96

Critical value for a two tailed test.

85

5%

One tailed test

85

5%

One tailed test

Z score where 5% of the distribution lies in the tail:

Z = + 1.65

Critical value for a one tailed test.

Z scores require and

What happens when the population mean is known but the standard deviation is unknown?

T test for single samples

XS

Xt

is the standard error of the mean, estimated.

XS

n

SSX

n

SSX

S is representing the standard deviation of the sample, as an estimate of the population.

1

2

n

XXS

n - 1 represents degrees of freedom. (df)

Degrees of freedom: the number of values that are free to vary.

Computational Formula

Standard deviation of a sample as an estimate of the population.

1

2

2

nn

XX

S

Situation that calls for a t test for single samples:

1) Population mean is know n.

2) The standard deviation of the population is unknown.

3) A sample of a specific size is available.

Steps for a single sample t test:

1) compute the standard deviation as an estimate of the population.

2) compute the standard error estimated

3) compute t

4) evaluate the computed t value to determine if it is statistically significant.

The t distribution:

- Symmetric

- Flatter middle than a normal

distribution. Fatter tails.

Xs

Xt

1

2

2

nn

XX

s

11010

63742197

2

s

11010

40576942197

s

9

9.4057642197 s

9

1.1620s

42.13s

n

SSX

10

42.13XS

16.3

42.13XS

24.4XS

24.4

807.63 t

24.4

3.16t

84.3t

Critical value = 2.262