Answer:
1. The required information are
The average annual bonuses,
received by employees from company A
The average annual bonuses,
received by employees from company B
The standard deviation, σ₁, of the average annual bonuses for employees from company A
The standard deviation, σ₂, of the average annual bonuses for employees from company A
The number of employees in company A, n₁
The number of employees in company B, n₂
2. The null hypothesis is H₀:
-
≤ 100
The alternative hypothesis is Hₐ:
-
> 100
Step-by-step explanation:
1. The required information are
The average annual bonuses,
received by employees from company A
The average annual bonuses,
received by employees from company B
The standard deviation, σ₁, of the average annual bonuses for employees from company A
The standard deviation, σ₂, of the average annual bonuses for employees from company A
The number of employees in company A, n₁
The number of employees in company B, n₂
2. The null hypothesis is H₀:
-
≤ 100
The alternative hypothesis is Hₐ:
-
> 100
The z value for the hypothesis testing of the difference between two means is given as follows;
![z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}-\frac{\sigma _{2}^{2}}{n_{2}}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%28%5Cbar%7Bx%7D_%7B1%7D-%5Cbar%7Bx%7D_%7B2%7D%29%7D%7B%5Csqrt%7B%5Cfrac%7B%5Csigma_%7B1%7D%5E%7B2%7D%20%7D%7Bn_%7B1%7D%7D-%5Cfrac%7B%5Csigma%20_%7B2%7D%5E%7B2%7D%7D%7Bn_%7B2%7D%7D%7D%7D)
At 0.5 level of significance, the critical
= ± 0
The rejection region is z >
and z < -
Therefore, the value of z obtained from the relation above more than or less than 0, we reject the null hypothesis, and we fail to reject the alternative hypothesis.