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

# Chapter 10: Analysis of Variance (ANOVA)

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

1) *F*_{crit}(3, 10) = +3.71

*F*(3, 10) = 0.3, *p *>.05

Figure 10.1

2) *F*_{crit}*(*4, 55*)* = +2.56

*F*(4, 55) = 11.25, *p* < .05

Figure 10.2

3) Figure 10.3

**RQ**: Do any of the website designs produce different viewing times from the other website designs?

*H*_{0}: *μ*_{1} = *μ*_{2} = *μ*_{3} = *μ*_{4 }= *μ*_{5 }= *μ*_{6}

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

*α* = .05

*F*_{crit}(5, 27) = +2.57 (Excel) or *F*_{crit}(5, 27) = +2.76 (by hand)

*F*(5, 27) = 11.09, *p *<.05

*η*^{2} = 0.67

**Conclusion:** Reject the null and accept the alternative. The ratio is statistically significant. At least two website designs have different means. Website design accounts for 67% of the total variance in viewing times. In post-hoc analyses, three homogeneous subgroups were identified. The first subgroup, containing Designs B, E and H, resulted in longer viewing times than the second subgroup, containing Designs B, C, E and F, which resulted in longer viewing times than the third subgroup, containing Designs C, F and G.

4) Figure 10.4

**RQ**: Do customers tip differently depending on the time of day?

*H*_{0}: *μ*_{1} = *μ*_{2} = *μ*_{3}

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

*α* = .05

*F*_{crit}(2, 18) = +3.55

*F*(2, 18) = 2.81, *p* > .05

**Conclusion:** Retain the null. The ratio is not statistically significant. There is not sufficient evidence to conclude that customers tip differently based on time of day.