A multiple choice test 30 questions, and each question has 5 answer choices (exactly one of which is correct). A student taking
1 answer:
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Answer:
Two tailed test
Parameter tested= population standard deviation
Step-by-step explanation:
1) Important concepts
The chi-square test if the standard deviation of a population is equal to a given value. We can conduct the test two-side or a one-side.
For the case of two-side we want to check if the population deviation is equal to some value or no. And for the case of one-side we want to check if the population devition is higher or lower than a given value.
The system of hypothesis are:
Null hypothesis
Alternative hypothesis
That's when we use the two sided version but we can have other's alternative hypothesis if we use one-side test:
Alternative hypothesis
Alternative hypothesis
The test statistic to check the hypothesis is:
For this special case the value of
Where N represent the sample size and s is the sample standard deviation. The ratio is important since allows to compare the ratio of the sample standard deviation to the specified value. If this ratio is different from 1, we will have evidence that we can reject the null hypothesis.
Using a significance level we can find the critical region for the possible alternative hypothesis:
for the upper one tailed option
for the lower one tailed option
for the two tailed option
The N-1 represent the degrees of freedom for the chi square distribution.
2) Solving the question
Based on all the info from above we can conclude that:
Type of test= Two tailed test
Parameter tested=population Standard deviation
And they want to check if the population deviation differs from 99
Find the powers
$a^{2}=5+2 \sqrt{6}$
$a^{3}=11 \sqrt{2}+9 \sqrt{3}$
The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.
Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$
so fits with the other answers.