In: Statistics and Probability
After 6 weeks following a Keto diet, Sam wants to know if there is a difference between the weight loss in men compared to the weight loss in women. After 6 weeks, a sample of 40 men showed a mean weight loss of 17.2 pounds while a sample of 55 women showed a mean weight loss of 13.4 pounds. The standard deviation of weight loss in men and women is 5.5 pounds and 3.9 pounds respectively. Using the 0.01 significance level, is there a difference between the weight loss in men compared to the weight loss in women.
Please use the five-step hypothesis test and show all workings.