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Gwar [14]
3 years ago
12

The math department recently purchased new learning software for their freshman math classes. The instructors want to use the le

arning software instead of a textbook. So they decide to study the effectiveness of the software. First they test the skills and concept mastery for a number of the freshman math students. Then they randomly divide the students into two groups. One group uses the learning software for a particular lesson and the other group uses the regular textbook. Then the instructors retest all of the students and compare the improvement in the skills and concept mastery for the two groups. What is the purpose of random assignment in this experiment? Check all that apply.
Mathematics
1 answer:
shusha [124]3 years ago
4 0

Options :

A.) To avoid bias

B. To control for confounding variables

C. To produce treatment groups with similar characteristics

D. To generalize the experiment results to all freshman math students

Answer:

To avoid bias

To generalize the experiment results to all freshman math students

Step-by-step explanation:

One of the most common problems with statistical experimental research is the issue posed by bias. Either selection bias or assignment bias. Bias creeps into our experiment when one experimental group is more favored than the other. This means that the strategy employed is not totally random. In the experimetal design explained above, students were randomly assigned to group in other to avoid bias. This random assignment ensures that all samples have equal probability of being assigned to any of the two groups.

Randomized experimental designs also allows for making a good estimate of the population parameter fromnthe sample statistic

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Given f(x)=x^2+2x+3 and g(x)=x+4/3 solve for f(g(x)) when x=2
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Answer:

\displaystyle\mathsf{f(g(2)) \:=\:\frac{187}{9}}

Step-by-step explanation:

We are provided with the following functions:

f(x) = x² + 2x + 3

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The given problem also requires to find the Composition of Functions, f(g(x)) when x = 2.

The <u>Composition of Function</u> <em>f</em> with function <em>g</em> can be expressed as ( <em>f ° g </em>)(x) = f(g(x)).  In solving for the composition of functions, we must first evaluate the <em>innermost</em> function, g(x), then use the output as an input for f(x).

<h2>Solve for f(g(x)) when x = 2:</h2><h3><u>Find g(x):</u></h3>

Starting with g(x), we will use x = 2 as an <u>input</u> value into the function:

\displaystyle\mathsf{ g(x)\:=\:x+\frac{4}{3} }

\displaystyle\mathsf{ g(2)\:=\:(2)+\frac{4}{3} }

Transform the first term, x = 2, into a fraction with a denominator of 3 to combine with 4/3:

\displaystyle\mathsf{ g(2)\:=\:\frac{2\: \times\ 3}{3}+\frac{4}{3} }

\displaystyle\mathsf{ g(2)\:=\:\frac{6}{3}+\frac{4}{3}\:=\:\frac{6+4}{3}}

\displaystyle\mathsf{ g(2)\:=\:\frac{10}{3} }

\displaystyle\mathsf{Therefore,\:\: g(2)\:=\:\frac{10}{3} }

<h3><u>Find f(x):</u></h3>

Next, we will use  \displaystyle\mathsf{\frac{10}{3}}&#10; as input for the function, f(x) = x² + 2x + 3:

f(x) = x² + 2x + 3

\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg)\:=\:x^2 \:+ 2x\:+\:3}

\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{10}{3}\Bigg)^{2}\:+ 2\Bigg(\frac{10}{3}\Bigg) \:+\:3}

Use the <u>Quotient-to-Power Rule of Exponents</u> onto the <em>leading term </em>(x²):

\displaystyle\mathsf{Quotient-to-Power\:\:Rule:\:\: \Bigg(\frac{a}{b}\Bigg)^m\:=\:\frac{a^m}{b^m} }

\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{10\:^2}{3\:^2}\Bigg)\:+ 2\Bigg(\frac{10}{3}\Bigg) \:+\:3}

Multiply the numerator (10) of the middle term by 2:

\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{100}{9}\Bigg)\:+ \Bigg(\frac{20}{3}\Bigg) \:+\:\frac{3}{1}}

  • Determine the <u>least common multiple (LCM)</u> of the denominators from the previous step: 9, 3, and 1 (which is 9).
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                       \displaystyle\mathsf{\frac{20}{3}\Rightarrow \:\frac{20\:\times\ 3}{3\:\times\ 3} =\:\frac{60}{9}}

                        \displaystyle\mathsf{\frac{3}{1}\Rightarrow \:\frac{3\:\times\ 9}{1\:\times\ 9} =\:\frac{27}{9}}

Finally, add the three fractions on the right-hand side of the equation:

\displaystyle\mathsf{f\Bigg (\frac{10}{3}\Bigg) \:=\:\Bigg (\frac{100}{9}\Bigg)\:+ \Bigg(\frac{60}{9}\Bigg) \:+\:\frac{27}{9}\:=\:\frac{187}{9}}

<h2>Final Answer:</h2>

\displaystyle\mathsf{Therefore,\:\:f(g(2)) \:=\:\frac{187}{9}.}

<h3>______________________________</h3>

<em>Keywords:</em>

Composition of functions

f o g

f (g(x))

____________________________________

Learn more about <u><em>Composition of Functions</em></u> here:

brainly.com/question/11388036

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