Please show work for better understanding Paige and Frankie are competing in a f
ID: 3294262 • Letter: P
Question
Please show work for better understanding Paige and Frankie are competing in a friendly rivalry of who can make the most profit from selling lemonade. The table below gives the sample of quantity of sales of glasses of lemonade each made across 5 days (suppose sales are normally distributed). Paige sells her lemonade at 50 cents each and Frankie sells hers at 70 cents each How many glasses of lemonades did each sell? b) Who made an absolute larger profit? c) Write a null and alternative hypothesis if one was more profitable than anotherExplanation / Answer
a. From given data, Paige sold 850 (160+210+90+150+240) glasses of lemonade across 5 days, and Frankie sold 600 (110+150+90+100+150) glasses of lemonade across 5 days.
b. It is given that Piage sold her lemonade at 50 cents each and Frankie sold her lemonade at 70 cents each. Therefore, total money received by Paige is 850*50=42500 cents and by Frankie is 600*70=42000 cents. Assuming the cost to make 1 glass of lemonade is same for both, Paige made an absolute larger profit (42500-42000=500).
c. The null hypothesis is the hypothesis of no difference, which states that there is no difference in absolute profit for Paigie and Frankie. The alternative hypothesis argues that Paigie has higher absolute profit than Frankie. Therefore, the hypotheses are as follows:
H0:muP-muF=0
Ha:muP-muF>0
This is a right-tailed test, as the alternative hypothesis uses > sign.