5) A newspaper article suggested that there is a relationship between grams of f

Question

5) A newspaper article suggested that there is a relationship between grams of fat and calories in a frozen dinner. To evaluate this claim you find the grams of fat and calories for 16 different frozen dinners. The data appear in the Dinners worksheet of the HW13 data workbook on Moodle.

a) What is the spearman correlation for Fat and Calories.

b) What is the appropriate null and alternate hypothesis to determine if the grams of fat and calories of a frozen dinner have a significant Spearman correlation?

c) Choose a level of Use = 0.05 for this problem.

d) Sketch the sampling distribution. Include the critical value and test statistic

e) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.

f) What is the p-value for the hypothesis test.

Company Dinner/Entree Fat (g) Calories Budget Gourmet French Recipe Chicken 9 240 Budget Gourmet Chicken au Gratin 11 250 Budget Gourmet Light Stuffed Turkey Breast 6 230 Budget Gourmet Light Chicken Breast Parmigiana 8 260 Budget Gourmet Light Teriyaki Chicken Breast 6 270 Freezer Queen Sliced Turkey Dinner 8 280 Healthy Choice Chicken Fettucine 4 240 Kraft Eating Right Macaroni and Cheese 8 270 Kraft Eating Right Beef Pepper Steak 10 290 Lean Cuisine Chicken in BBQ Sauce 6 260 Swanson Hungry Man Salisbury Steak Dinner 36 640 Tyson Chicken Français 14 280 Weight Watchers Filet of Fish au Gratin 6 200 Weight Watchers Beef Sirloin Tips 7 220 Weight Watchers Chicken Fajitas 1 230 Weight Watchers Lasagna with Meat Sauce 10 320

Explanation / Answer

I am using R software to solve the problem

At first, we can create 2 vectors for Fat and Calories as below:

Fat <- c(9,11,6,8,6,8,4,8,10,6,36,14,6,7,1,10)
Calories <- c(240,250,230,260,270,280,240,270,290,260,640,280,200,220,230,320)

a) Spearman correlation can be found using cor() function in R as below:

cor(Fat,Calories,method="spearman")

=0.6753919

b) Null hypothesis - There is no relationship i.e. the correlation between grams of fat and calories in the population is zero.

Alternative Hypothesis - There exists a relationship between grams of fat and calories in the population i.e. correlation is not zero.

c) We can test for statistical significance of the correaltion using cor.test() function in R as below. We are interested in two sided test here.

cor.test(Fat,Calories,alternative = "two.sided",method="spearman")

   Spearman's rank correlation rho

data: Fat and Calories
S = 220.73, p-value = 0.004089
alternative hypothesis: true rho is not equal to 0
sample estimates:
rho
0.6753919

e) Conclusion is that as p value is less than 0.05, we reject the null hypothesis i.e. we conclude that there exists a relationship between grams of fat and calories in population.

f) The p value of the hypothesis test is 0.004089 as mentioned above.

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