1. **State the problem:** We want to test if the average calorie burn per session for users with personalized workout plans ($M_1$) is higher than for users without personalized plans ($M_2$). 2. **Set hypotheses:** $$H_0: M_1 - M_2 = 0$$ $$H_a: M_1 - M_2 > 0$$ 3. **Given data:** - Sample size with plan: $n_1 = 50$ - Sample mean with plan: $\bar{x}_1 = 300$ - Sample standard deviation with plan: $s_1 = 120$ - Sample size without plan: $n_2 = 60$ - Sample mean without plan: $\bar{x}_2 = 260$ - Sample standard deviation without plan: $s_2 = 90$ - Significance level: $\alpha = 0.05$ 4. **Check conditions:** - Random samples: confirmed - Independent samples: confirmed - Normality or large sample size: $n_1 > 30$ and $n_2 > 30$ satisfy Central Limit Theorem 5. **Test statistic formula for two-sample t-test:** $$t = \frac{(\bar{x}_1 - \bar{x}_2) - (M_1 - M_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$$ 6. **Calculate test statistic:** $$t = 1.94$$ (given) 7. **Degrees of freedom:** $$df = 89.4$$ (given) 8. **P-value:** $$p = 0.027$$ (given) 9. **Decision:** Since $p = 0.027 < \alpha = 0.05$, we reject the null hypothesis. 10. **Conclusion:** There is significant evidence to suggest that the average calorie burn per session among users with personalized plans is higher than among those without personalized plans. **Part b)** 11. **Type of error possible:** Since we rejected $H_0$ when it might be true, the possible error is a **Type I error**. 12. **Explanation:** A Type I error means concluding that personalized plans increase calorie burn when in fact there is no real difference in the population.