Advanced Higher

STATISTICS

Student’s t-test(testing the difference between 2 samples)

t = Ẋ- ӯ √(SE of x)2 + (SE of y)2

A student’s t-test is a test of the difference between two samples. It is applied only to data measured on an interval or ratio scale.

- The null hypothesis is always that the two samples are the same.- The alternative hypothesis states that the two means are

different.

Advanced Higher

STATISTICS

Is there a difference between the two sets of data?

1 2 3 4 5 6 7 8 90

5

10

15

20

Series1Sw

itzerland

Germ

any

Norw

ay

France

Japan

New

Zealand

USA

Spain

Italy

1 2 3 4 5 6 7 8 90

10

20

30

40

50

60

Series1

Colombia

Zambia

Egypt

Kenya

India

Brazil

Bangladesh

Ethiopia

Mali

BIRTH RATE IN LEDCs BIRTH RATE IN MEDCs

Use the students t-test to see if there is a significant difference, or not.

Null Hypothesis: there is no significant difference between the mean birth rates of more developed and less developed countries.Alternative Hypothesis: there is a significant difference between the mean birth rates of more developed and less developed countries.

-2-4

4161

40

116

44

Switzerland - 12

Germany - 10Norway - 13France - 14

Japan - 16

New Zealand - 18

USA - 15

Spain - 16

Italy - 12

1269

14

50

5.56

2.36

-1011-5

-58

-7-11

109

10012125

2564

49121

10081

Colombia - 30

Zambia - 51Egypt - 35Kenya - 48

India - 35

Brazil - 29

Bangladesh - 33

Ethiopia - 50

Mali - 49

1269

14

686

76.2

8.73

-1

20

14

2-2

2.36√9√

8.73√9√

0.786 2.910

Use the students t-test to see if there is a significant difference, or not

Null Hypothesis: there is no significant correlation between percentage of soil moisture and altitude.Alternative Hypothesis: there is a significant correlation between percentage of soil moisture and altitude.

t = Ẋ- ӯ √(SE of x)2 + (SE of y)2

t = 14 - 40 √0.617 + 8.469

t = -26 √9.086

t = -8.625

NOTE: The t-value can be positive or negative. For this test we can ignore the sign and just use the figure when we compare it against the critical value

Now look to see if the calculated value of t is

higher or lower than the critical value.

Null Hypothesis: there is no significant correlation between percentage of soil moisture and altitude.Alternative Hypothesis: there is a significant correlation between percentage of soil moisture and altitude.

t = -8.625

Calculate degrees of freedom (nx – 1) + (ny – 1)

(9-1) + (9-1) = 16

16

The calculated value of t is 8.62 which is higher than the critical value of 2.12 (95% confidence) and 2.92 (99%) so we can reject the null hypothesis and

accept the alternative hypothesis that there is a significant difference between developing and developed countries birth rates.