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muminat
3 years ago
7

A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects

were followed for 12 months. Weight change for each subject was recorded. The researcher wants to test the claim that all ten programs are equally effective in weight loss. (a) Which statistical approach should be used? (i) confidence interval (ii) t-test (iii) ANOVA (iv) Chi square (b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach?
Mathematics
1 answer:
Yakvenalex [24]3 years ago
8 0

Answer:

a) (iii) ANOVA

b) The ANOVA test is more powerful than the t test when we want to compare group of means.

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

If we assume that we have p=10 groups and on each group from j=1,\dots,p=10 we have n_j individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2

And we have this property

SST=SS_{between}+SS_{within}

Solution to the problem

Part a

(i) confidence interval

False since the confidence interval work just when we have just on parameter of interest, but for this case we have more than 1.

(ii) t-test

Can be a possibility but is not the best method since every time that we conduct a t-test we have a chance that we commit a Type I error.

(iii) ANOVA

This one is the best method when we want to compare more than 1 group of means.

(iv) Chi square

False for this case we don't want to analyze independence or goodness of fit, so this one is not the correct test.

Part b

The ANOVA test is more powerful than the t test when we want to compare  group of means.

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−8 3/4÷2 1/6 please show me ur work
nalin [4]

Answer:

  • - 4 1/26

Step-by-step explanation:

<u>Solving in steps:</u>

  • - 8 3/4 ÷ 2 1/6 =
  • - 35/4 ÷ 13/6 =
  • - 35/4 × 6/13 =
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6 0
3 years ago
Explain why ΔABC cannot be shown to be congruent to ΔCDA.
igomit [66]

There isn't enough info to prove the triangles to be congruent or not. So we can't say for sure either way.

We have angle CAD = angle ACB given by the arc markings, and we know that AC = AC due to the reflexive theorem. However we are missing one third piece of information.

That third piece of info could be....

  • AD = BC which allows us to use SAS
  • angle ACD = angle CAB which allows us to use ASA
  • angle ABC = angle CDA which allows us to use AAS (slight variation of ASA)

Since we don't know any of those three facts, we simply don't have enough information.

side note: If AB = CD, then this leads to SSA which is not a valid congruence theorem. If we had two congruent sides, the angle must be between the two sides, which is what AD = BC allows.

4 0
2 years ago
The hypotenuse of a right triangle is 7 inches,and one of the legs is 13 inches.Find the length of the other leg.
Firlakuza [10]
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6 0
3 years ago
I need help with this one <br><br><br><br> Q13
horsena [70]

Answer:

x= 2 5/6

Step-by-step explanation:

1/3= 2/6

2 1/2= 2 3/6

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Hope this helps! :)

6 0
2 years ago
Read 2 more answers
a storeroom 21 feet long, 15 feet wide, and 11 feet high was enlarged to a length of 25 feet and a width of 17 feet. how many cu
xenn [34]
<h2>1210 cubic feet</h2>

Step-by-step explanation:

       Initial dimensions of the storeroom were 21\text{ }ft length, 15\text{ }ft width and 11\text{ }ft height.

       The room is in the shape of a cuboid. Volume of a cuboid = V=l\times b\times h, where l,b,h are the length, width and height of the cuboid.

       So, Volume of storeroom initially = 21\text{ }ft\text{ }\times15\text{ }ft\text{ }\times11\text{ }ft\text{ }=3465\text{ }ft^{3}\text{ }

       Finally, the length was increased to 25\text{ }ft and width to 17\text{ }ft.

       Final volume of storeroom = 25\text{ }ft\text{ }\times 17\text{ }ft\text{ }\times 11\text{ }ft\text{ }=4675\text{ }ft^{3}\text{ }

       Increase in volume = 4675\text{ ft}^{3}-3465\text{ ft}^{3}=1210\text{ ft}^{3}

∴ 1210 cubic feet of storage was added.

7 0
3 years ago
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