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Answer:
The best way to know weather the formula y=x⁴-4x³+3x² is growing or not, is by graphing it.
As you can see in the attached picture:
- For -inf<x< 0 the graph decreases.
- For 0<x<0.634 the graph is growing
- For 0,634<x<2.366 the graph decreases
- For 2.366<x<+inf the graph is growing.
Therefore, the polynomial grows in the intervals stated before.
Using the equation of the test statistic, it is found that with an increased sample size, the test statistic would decrease and the p-value would increase.
<h3>How to find the p-value of a test?</h3>
It depends on the test statistic z, as follows.
- For a left-tailed test, it is the area under the normal curve to the left of z, which is the <u>p-value of z</u>.
- For a right-tailed test, it is the area under the normal curve to the right of z, which is <u>1 subtracted by the p-value of z</u>.
- For a two-tailed test, it is the area under the normal curve to the left of -z combined with the area to the right of z, hence it is <u>2 multiplied by 1 subtracted by the p-value of z</u>.
In all cases, a higher test statistic leads to a lower p-value, and vice-versa.
<h3>What is the equation for the test statistic?</h3>
The equation is given by:
The parameters are:
is the sample mean.
is the tested value.
- s is the standard deviation.
- n is the sample size.
From this, it is taken that if the sample size was increased with all other parameters remaining the same, the test statistic would decrease, and the p-value would increase.
You can learn more about p-values at brainly.com/question/26454209