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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Transcript of H1H1 H1H1 HoHo Z = 0 Two Tailed test. Z score where 2.5% of the distribution lies in the tail: Z = +...
![Page 1: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/1.jpg)
H1H1
Ho
Z = 0
Two Tailed test
![Page 2: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/2.jpg)
Z score where 2.5% of the distribution lies in the tail:
Z = + 1.96
Critical value for a two tailed test.
![Page 3: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/3.jpg)
85
5%
One tailed test
![Page 4: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/4.jpg)
85
5%
One tailed test
![Page 5: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/5.jpg)
Z score where 5% of the distribution lies in the tail:
Z = + 1.65
Critical value for a one tailed test.
![Page 6: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/6.jpg)
Z scores require and
What happens when the population mean is known but the standard deviation is unknown?
![Page 7: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/7.jpg)
T test for single samples
XS
Xt
![Page 8: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/8.jpg)
is the standard error of the mean, estimated.
XS
n
SSX
n
SSX
![Page 9: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/9.jpg)
S is representing the standard deviation of the sample, as an estimate of the population.
1
2
n
XXS
![Page 10: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/10.jpg)
n - 1 represents degrees of freedom. (df)
Degrees of freedom: the number of values that are free to vary.
![Page 11: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/11.jpg)
Computational Formula
Standard deviation of a sample as an estimate of the population.
1
2
2
nn
XX
S
![Page 12: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/12.jpg)
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.
![Page 13: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/13.jpg)
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.
![Page 14: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/14.jpg)
The t distribution:
- Symmetric
- Flatter middle than a normal
distribution. Fatter tails.
![Page 15: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/15.jpg)
Xs
Xt
![Page 16: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/16.jpg)
![Page 17: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/17.jpg)
1
2
2
nn
XX
s
![Page 18: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/18.jpg)
![Page 19: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/19.jpg)
11010
63742197
2
s
![Page 20: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/20.jpg)
11010
40576942197
s
![Page 21: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/21.jpg)
9
9.4057642197 s
![Page 22: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/22.jpg)
9
1.1620s
42.13s
![Page 23: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/23.jpg)
n
SSX
![Page 24: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/24.jpg)
10
42.13XS
16.3
42.13XS
24.4XS
![Page 25: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/25.jpg)
24.4
807.63 t
24.4
3.16t
![Page 26: H1H1 H1H1 HoHo 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.](https://reader033.fdocuments.in/reader033/viewer/2022051620/56649ece5503460f94bdbe0c/html5/thumbnails/26.jpg)
84.3t
Critical value = 2.262