The following table shows the daily calories intake for two groups of samples who said they normally do not eat fast food and usually eat fast food: eat fast food sample size sample mean sample standard deviation
No 663 2258 1519
Yes 413 2637 1138

We are interested in exploring whether this data provide strong evidence for concluding that average calorie intake for people who eat fast food is larger than the those who do not usually eat fast food.

Required:
a. What are the null hypothesis and alternative hypothesis?
b. Use central limit theorem to find the p-value and make a decision based on α = 0.05 significance level.
c. Use Welch’s t test to find the p-value and make a decision based on α = 0.05 significance level. (Use R to help you find the p-value for this problem).