# A Step-by-Step Introduction to Statistics for Business

# Chapter 13: Matching Statistical Tests to Business Problems

Answers for **Data Skill Challenges** for every chapter in the book can be found to check your performance and widen your understanding.

1) **RQ:** Is job performance now less than job performance six months ago?

*H*_{0}: *μ*_{d }≥ 0

*H*_{1}: *μ*_{d }< 0

where

α = .05

*t*_{crit}(150) = −1.655

*t*(149) = −1.24, *p* >.05 or *t*(149) = −1.24, *p* = .11

CI_{95} = [−0.03, 0.14]

**Conclusion:** Retain the null. The difference was not statistically significant. There is insufficient evidence to conclude that job performance now is less than it was six months ago. If we assume this sample mean difference to represent the population mean difference, we would expect 95% of sample means to fall between −0.32 and 0.14.

2)** RQ: **Are our employees drawn from a population where employees are 31 years old?

*H*_{0}: *μ* = 31

*H*_{1}: *μ* ≠ 31

*α* = .05

*t*_{crit}(150) = ±1.976

*t*(149) = –24.22, *p* < .05

CI_{95} = [24.46, 25.45]

diff = 31 – 24.95 = 6.05

**Conclusion: **Reject the null. The difference was statistically significant. Our employees are not drawn from a population where employees are 31 years old. If we assume this sample to represent the population, we would expect 95% of sample means to fall between 24.46 and 25.45. Our employees are on average 6.05 years younger than the given population.

3) **RQ**: Do the ages of employees differ by department?

*H*_{0}: *μ*_{1} = *μ*_{2} = *μ*_{3} = *μ*_{4} = *μ*_{5}

*H*_{1}: At least two means differ

*α* = .05

*F*_{crit}(4, 100) = +2.46

*F*(4, 145) = 0.97, *p *>.05

**Conclusion:** Retain the null. The ratio is not statistically significant. The ages of the employees do not differ by department

Figure 13.3

4) **RQ _{2}: **Are there more women in relation to men in some departments?

*H*_{0}: Gender is independent of department.

*H*_{1}: Gender is not independent of department.

*α* = .05

*c*^{2}(4)_{crit} = +9.488

*c*^{2}(4) = +3.20, *p* > .05

**Conclusion:** Retain the null. The chi-squared was not statistically significant. Department does not differ by gender.