Answer to Question #103694 in Statistics and Probability for Nathan

Question

2. ten person were appointed in a clerical position in an office. Their performance was noted by giving a test and marks recorded out of 50. They were given 6 months training and and again they were given a test marks were recorded out of 50.

Employees

A

B

C

D

E

F

G

H

I

J

Before training

25

20

35

15

42

28

26

44

35

48

After training

26

20

34

13

43

40

29

41

36

46

Apply the t.test can you conclude that the employees benefitted by the training.you are given ᾳ 5 %.

Answer 1

Paired sample t-test is used.

For the difference in scores After-Before:

$n=10,\;\bar{x}=1,\;s=4.27.$

Null hypothesis $H_0:\;\mu_d=0.$

Alternative hypothesis $H_a:\;\mu_d>0.$

Test statistic: $t=\frac{\bar{x}}{\frac{s}{\sqrt{n}}}=\frac{1}{\frac{4.27}{\sqrt{10}}}=0.74.$

Degrees of freedom: $df=n-1=10-1=9.$

P-value: $p=P(T>0.74)=0.2391.$

Since P-value is greater than 0.05, fail to reject the null hypothesis.

There is no sufficient evidence that the employees benefited by the training.