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

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".

Step-by-step 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              

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".

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

2 x 503

step-by-step explanation:

its 1006