Answer to Question #209201 in Statistics and Probability for beena

Question

samples of 12 foremen in one division and 10 foremen in another division of a factory were selected at random and the following data were obtained.

Sample Size Average monthly salary (Rs.) S.D. of salary (Rs.)

Division I 12 6000 150

Division II 10 5500 165

Can you conclude that the foremen in division I get more salary than foremen in division II at 5% level ?

Answer 1

Given, $n_1=12,x_1=6000,\sigma_1=150$

$n_2=10,x_2=5500,\sigma_2=165$

Let $H_o:$ foremen in division I get more salary than foremen in division II at 5% level.

and $H_a:$ foremen in division I do not get more salary than foremen in division II at 5% level.

Here we use t-test for two independent samples-

$t=\dfrac{x_1-x_2}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}=\dfrac{6000-5500}{\sqrt{\frac{150^2}{12}+\frac{165^2}{10}}}=\dfrac{500}{67.80}=7.3746$

The formula to calculate degree of freedom is-

Here degree of freedom $= n_1+n_2-2=12+10-2=20$

The value of t at 5% significance level and degree of freedom 20 is 1.725

Conclusion: The calculated value of t is greater tan the standard value at 5% significance level. So $H_o$ is rejected i.e. foremen in division I do not get more salary than foremen in division II