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ratelena [41]
3 years ago
13

Alicia is writing the program for a video game. For one part of the game she uses the rule ( x , y) ----> ( x - 3, y + 4) to

move points on the screen.
(1) What output does the rule give when the input is (-7, 0)? Show your work.

(2) What output does the rule give when the input is (2, -4)? Show your work.
Mathematics
1 answer:
anastassius [24]3 years ago
5 0
The "rule" being described here is nothing more than the input/output of a mathematical function. 

<span>For every input 'x' value supplied, you only need to subtract three to it. For every input 'y' value, you only need to add four to it. </span>

<span>Example: I'll use variable 'm' to represent this function. Variable 'p' will represent the current input point. </span>

<span>m(p) = p[x - 3, y + 4] = p[-7 - 3, 0 + 4] = p[-10, 4]. 'p[]" is just the point.</span>
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The test statistic is z = -2.11.

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Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

H_0: \mu_1 - \mu_2 = 0

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

H_1: \mu_1 - \mu_2 \neq 0

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

From the two samples:

X = \mu_1 - \mu_2 = 1276 - 1439 = -163

s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144

Test statistic:

z = \frac{X - \mu}{s}

z = \frac{-163 - 0}{77.3144}

z = -2.11

The test statistic is z = -2.11.

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