Question

The number of grams of carbohydrates contained in 5–ounce of randomly selected meals "with/with no" potatoes (fries) in McDonald's restaurant is listed below. Is there sufficient evidence to conclude that there is difference in mean carbohydrate content between "meals with potatoes" and "meals with no potatoes"? Use α = 0.01. Potatoes : 29 25 17 36 41 25 32 29 38 34 24 27 29 No Potatoes : 41 41 37 29 30 38 39 10 29 55 29 27 31

Answer 1

Answer:

Since the calculated value of t= -1.340 does not fall in the critical region , so we accept H0 and may conclude that the data do not provide sufficient evidence to indicate hat there is difference in mean carbohydrate content between "meals with potatoes" and "meals with no potatoes".

Explanation:

Potatoes : No Potatoes : Difference Difference (d)²

(Potatoes- No Potatoes)

29 41 -12 144

25 41 -16 256

17 37 -20 400

36 29 -7 49

41 30 11 121

25 38 -13 169

32 39 -7 49

29 10 19 361

38 29 9 81

34 55 -21 441

24 29 -5 25

27 27 0 0

29 31 -2 4

∑ -64 2100

1. We state our null and alternative hypotheses as

H0 : μd= 0 and Ha: μd≠0

2. The significance level alpha is set at α = 0.01

3. The test statistic under H0 is

t= d`/sd/√n

which has t distribution with n-1 degrees of freedom.

4. The critical region is t > t (0.005,12) = 3.055

5. Computations

d`= ∑d/n = -64/ 13= -4.923

sd²= ∑(di-d`)²/ n-1 = 1/n01 [ ∑di² - (∑di)²/n]

= 1/12 [2100- ( -4.923)] = 175.410

sd= √175.410 = 13.244

t = d`/sd/√n= - 4.923/13.244/√13

t= - 4.923/3.67344

t= -1.340

6. Conclusion :

Since the calculated value of t= -1.340 does not fall in the critical region , so we accept H0 and may conclude that the data do not provide sufficient evidence to indicate hat there is difference in mean carbohydrate content between "meals with potatoes" and "meals with no potatoes".