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3 years ago

The following data are from a completely randomized design.

Mathematics

1 answer:

Mila [183]3 years ago

7 0

Answer:

a)1488

b) 744

c) 2030

d) 135.333

e) see attached table

f) There is sufficient evidence to reject the claim of equal means.

Step-by-step explanation:

a) Determine the value of total-group variability SS(tot):

SS(tot)=∑x^2(tot)-(x(tot))^2/N=376766-2592^2/18 ≅ 3518

Determine the value of the sum of squares between groups:

SS(bet) = ∑_(all groups) (∑x_i)^2/n_i -(∑x(tot))^2/N

=936^2/6+852^2/6+804^2/6-2592^2/6≅ 1488

b) d.f(BET) is the number of groups k decreased by 1.

d.f(BET) = k - 1= 3-1 = 2

MS(BET) is SS(BET) divided by d.f(BET):

MS(BET)=SS(BET)/ d.f(BET)

=1488/2

=744

c) The value of the sum of squares within groups (due to error) is then the value of the total-group variability decreased by the value of the sum of squares between groups (Note: using this calculation you then immediately obtain that the sum SS(tot) =SS(bet)+ SS(W) holds):

SS(W) = SS(tot) - SS(bet) = 3518 - 1488 = 2030

d) d.f.w is the total sample size decreased by the number of groups k.

d.f.w = N — k = 18 — 3 = 15

MSw is SSw divided by d.f.w:

MSw =SSw/d.f.w=2030/15=135.333

e) see attached table

f) The value of the test statistic F is then MS(BET) divided by MSw:

F=MS(BET)/MSw=744/135.3333≅5.5

The degrees of freedom are the same as those for between groups and within groups:

d.f.N=d.f(BET)=2

d.f.D=d.f.w=15

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value in the row dfn = 2 and dfd = 15:

0.01<P<0.025

If the P-value is less than the significance level, reject the null hypothesis.

P<0.05==> Reject H_o

There is sufficient evidence to reject the claim of equal means.

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3 years ago

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NeTakaya

The answer in itself is 1/128 and here is the procedure to prove it:
cos(A)*cos(60+A)*cos(60-A) = cos(A)*(cos²60 - sin²A)

= cos(A)*{(1/4) - 1 + cos²A} = cos(A)*(cos²A - 3/4) 

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4 years ago

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I dont like C and D argument too much because being the best in a sport doesnt mean either that you reach the maximum level possible (in many cases you can keep growing) or that you dont have more motivations. Many athletes are super competitive people and they try to improve themselves all the time to reach, and stay, in the top.

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