h1h1 h1h1 hoho z = 0 two tailed test. z score where 2.5% of the distribution lies in the tail: z = +...
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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