Question

Employees from Company A and Company B both receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.05 level of significance? Write out the hypothesis and explain the testing procedure.

Answer 1

Answer)

Null hypothesis Ho : u1 - u2 <= 100

Alternate hypothesis Ha : u1 - u2 > 100

u1 = Average bonus for company A

u2 = average bonus for company B

Test statistics = ((x1-x2)-100)/standard error

Standard error = √{(s1^2/n1)+(s2^2/n2)}

X1 = sample mean of the sample from the company A

X2 = sample mean of the sample from the company B

S1 = sample s.d of sample 1 (company A)

S2 = sample s.d of sample 2 (Company B)

N1 = N2 = sample sizes

After substitution

We will get the test statistics

Now we need to look in to t table for degrees of freedom (smaller of n1-1,n2-1) and calculated test statistics for the p-value

If p-value is greater than 0.05,

Then we fail to reject the null hypothesis

In this case we would not have enough evidence to support the claim that u1 - u2 > 100

And if p-value is less than 0.05

We reject the null hypothesis

In this case we would have enough evidence o support the claim that u1-u2 > 100