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Vlad [161]
3 years ago
7

Identify the level of measurement of data and explain what is wrong with the given calculation. In a set of data car ranking rep

resented as 0 for first, 1 for second and 2 for third. The average (mean) of the 580 car ranking is 0.9
Mathematics
1 answer:
eimsori [14]3 years ago
8 0

There are different levels of measurement that have been classified into four categories. It is important for the researcher to understand the different levels of measurement, as these levels of measurement play a part in determining the arithmetic and the statistical operations that are carried out on the data.

In ascending order of precision, the four different levels of measurement are:

<span>nominalordinalinterval<span>ratio</span></span>
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A study randomly assigned adult subjects to one of three exercise treatments: (1) a single long exercise period five days per we
Katen [24]

Answer:

Step-by-step explanation:

Hello!

For this study adult subjects were randomly assigned to three different exercise treatments establishing three different groups:

Group 1: Single long exercise period five days per week

Group 2: Several 10' exercise periods five days per week

Group 3: Several 10' exercise periods five days per week using a home treadmill

All subjects were weighed before and after 6 months of training and their weight loss was determined.

The objective of this study is to determine if there is any difference between the treatments, meaning, if the weight loss is the same regarding the type of exercise or if the type of exercise has some influence over it.

To test this you have to conduct an ANOVA, with the hypothesis:

H₀: μ₁= μ₂= μ₃

H₁: At least one μi differs from the others. ∀ i=1, 2, 3

α: 0.05

The statistic is:

F= \frac{MS_{Tr}}{MS_{Er}} ~~F_{k-1; n-k}

Normally it is better to have the raw data to conduct the analysis using statistical software, but it is not impossible to calculate the statistic using the descriptive statistics for each group.

As you know the statistic is calculated as the ratio between the mean square of the treatments (between groups) and the mean squares of errors.

Each means square is calculated as the sum of squares by the degrees of freedom of the category: SS/Df

So first you need to determine the SS and Df of treatments and errors, then the MS and finally the value of F.

Treatments:

> The degrees of freedom between treatments are k-1 (k represents the number of treatments):

DfTr: 3-1= 2

>The sum of squares is:

SSTr: ∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= grand mean is the mean that results of all the groups together.

So the Sum of squares of treatments (SSTr) is the sum of the square of the difference between the sample mean of each group and the grand mean.

To calculate the grand mean you can sum the means of each group and dive it by the number of groups:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ k = (10.2+9.3+10.2)/3= 29.7/3= 9.9

SSTr= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (10.2 - 9.9)² + (9.3 - 9.9)² + (10.2 - 9.9)²= 0.54

> The Means Squares is:

MSTr= SSTr/DFTr= 0.54/2= 0.27

Errors

>Degrees of freedom of error DfEr= N-k Where N is the total of observations of the experiment (N= n₁+n₂+n₃) and k is the number of treatments.

DfEr= N-k= 30-3= 27

>The mean square error (MSEr) is the estimation of the variance error (σ_{e}^2 → S_{e}^2), you have to use the following formula:

S_{e}^2= \frac{(n_1-1)S^2_1+(n_2-1)S_2^2+(n_3-1)S^2_3}{N-k}= \frac{(9*17.64)+(9*20.25)+(9*27.04)}{27}= \frac{584.37}{27}= 21.643

Finally you calculate the statistic:

F_{H_0}= \frac{MS_{Tr}}{MS_{Er}}= \frac{0.27}{21.643}= 0.012

This test is One-tailed right, meaning that you'll reject to high values of the statistic and there is one critical value:

F_{k-1;N-k;1-\alpha }= F_{2;27;0.95}= 3.35

Using the critical value approach, the decision rule is:

If F_{H_0} ≥ 3.35, reject the null hypothesis.

If F_{H_0} < 3.35, do not reject the null hypothesis.

The calculated value is less than the critical value, the decision is to not reject the null hypothesis.

So at a 5% significance level, there is not enough evidence to conclude that the treatments influence significantly in weight loss. The population mean weight loss is the same for the treatments "Single long exercise period five days per week", "Several 10' exercise periods five days per week" and "Several 10' exercise periods five days per week using a home treadmill"

I hope this helps!

5 0
3 years ago
Change to Scientific Notation<br> .0000000005
zimovet [89]

5x10^-10 is the answer

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3 years ago
Eleven of 20 students in Mr. Gonzalez ‘s science class are attending the field trip. What percent best represents the portion of
antoniya [11.8K]

Answer:

%55

Step-by-step explanation:

divide both values by 2, multiply by 10 to give you a percentage


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Complementary I’m sure but I could be wrong
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