Question 2 People can become obsessed with body weight and d

Question 2 -People can become obsessed with body weight and diets nowadays, and

because the media are insistent on ramming ridiculous images of stick-thin celebrities

down into our eyes and brainwashing us into believing that these emaciated corpses

are actually attractive, we all end up terribly depressed that we are not perfect. This

gives evil corporate types the opportunity to jump on our vulnerability by making loads

of money on diets that will apparently help us attain the body beautiful. Well, not wishing

to miss out on this great opportunity to exploit people’s insecurities, Dr. Evil came up

with his own diet called the “Evil Diet”. The basic principle is that you eat like him: you

eat one lean meat (4 oz), eat greens (8 oz), drink lots of Darjeeling tea and water, and

eat the nutrition bar and shakes Dr. Evil created five times per day. To test the efficacy

of his wonderful new diet, he took 10 participants who considered themselves to be in

need to losing weight and put them on this diet for two months. Their weight was

measured in Kilograms at the start of the diet and then after 1 month and 2 months.

Table below are the data. Set the significant level at = .01.

Before Diet After 1 Month After 2 Months

63.75 65.38 81.34

62.98 66.24 69.31

65.98 67.70 77.89

107.27 102.72 91.33

66.58 69.45 72.87

120.46 119.96 114.26

62.01 66.09 68.01

71.87 73.62 55.43

83.01 75.81 71.63

76.62 67.66 68.60

(1) Ho: ___________________________________________________ (2 points)

(2) Ha: ___________________________________________________ (2 points)

(3) Appropriate statistical test. (2 points)

______________________________________________________________________

(4) What are the F-statistic, dfs, p-value, and effect size for the effect? (3 points)

______________________________________________________________________

(5) Do you need to conduct the follow up test? Why? If yes, report your follow up

tests results. (5 points)

(6) What is your decision about null hypothesis? (4 points)

(7) Verbal Conclusions (remember to include all information above). (5 points)

Solution

Ho: there is no significant difference between means of diets against H1:there is a significant difference between means of diets. Here we use F test at 0.01 level of significance with (2,27) degrees of freedom. TSS=189240.0035-180006.1956=9233.8079. SST=(60922.7081+60005.1637+59085.3569)-180006.1956=7.0331. ESS=TSS-SST=9233.8079-7.0331=9226.7748. F=MST/MSE=(7.033/2)/(9226.7748/27)=3.51655/341.7324=0.01029. The table value of F at (2,27) at 0.01 is 5.49. Here Fcal<Ftab, so we accept null hypothesis . Therefore, there is no significant difference between means of diets.