Question

a salary adjustment was given to two retail stores recently merged. Ten employees' salaries were recorded before and after the adjustment. The average difference was an increase of $2,250 with a standard deviation of $1,100. Test if the increase is significant at the .10 level?

Answer 1

: Average Difference in the salaries before and after(Difference : After-Before)

Null hypothesis :H_o : average difference = 0.0 (Average difference is not significant) ; = 0

Alternate hypothesis : Average difference > 0.0 (Average difference is significant) ; > 0

Right Tailed test

: Sample average difference = 2250

s_d : Sample standard deviation of difference = 1100

Sample size : n= 10

Degrees of freedom = n-1 = 10-1 =9

Level of significance : = 0.10

For Right Tailed test :

for 9 degrees of freedom : P(t>6.4683) = 0.0001

As P-Value i.e. is less than Level of significance i.e (P-value:0.0001 < 0.1:Level of significance); Reject Null Hypothesis

There is sufficient evidence to conclude that the average difference in salaries is more than 0.

i.e

There is sufficient evidence to conclude that increase is significant.