Improve Your Understanding of College Level Statistics Problems

$H_0\mathrm{\beta <!--\; \beta \; -->}=0,H_a\mathrm{\beta <!--\; \beta \; -->}\ne <!--\; \ne \; -->0$.
The test itself is a generalized likelihood ratio. The test statistic is the ratio LR:
$LR=\frac{L(\mathrm{\beta <!--\; \beta \; -->}=0)}{argma{x}_{\mathrm{\beta <!--\; \beta \; -->}\in <!--\; \in \; -->R}L(\mathrm{\beta <!--\; \beta \; -->})}$
Where $L$ is the likelihood function.Then $-<!--\; -\; -->2ln(LR)$ follows a ${\mathrm{\chi <!--\; \chi \; -->}}_1^2$.
I am trying to calculate the p-value for a specific value of LR. Say I look for at a ${\mathrm{\chi <!--\; \chi \; -->}}_1^2$ table (or online calc) and find out that
$P({\mathrm{\chi <!--\; \chi \; -->}}_1^2\ge <!--\; \ge \; -->-<!--\; -\; -->2ln(LR))=\mathrm{\alpha <!--\; \alpha \; -->}$
Is $\mathrm{\alpha <!--\; \alpha \; -->}$ my final $p$-value?
Or do I need to account for the fact that the test is two-sided and set the $p$-value $=2\ast <!--\; \ast \; -->\mathrm{\alpha <!--\; \alpha \; -->}$?

How do you find the mean and median of 136, 129, 128, 122, 134, 120?

I have a question as follows:
Assuming the null hypothesis is true for all cases. If we perform multiple pairwise comparisons at the $\mathrm{\alpha <!--\; \alpha \; -->}=0.05$ level, what is the probability of making type I error with AT LEAST ONE of the tests?
The correct answer is greater than 0.05, and I don't know why. Thanks in advance!

To test for the significance of a Pearson correlation, one must use the ______________ distribution.
Group Answer Choices:
1. F
2. Chi-square
3. z
4. t

Determine the following situations then, what type of random or non random sampling technique is used. 1. Selected vehicle are classified according to the last number of their plates as odd or even. 2. There are 30 freshmen, 20 sophomores, 10 juniors, and 5 seniors enrolled in a certain course. Samples are to be taken from them according to the total number of students per year level. 3. Minority groups of senators are to be interviewed 4. Every five files out 500 files will be chosen 5. Animals going to astray are to be observed. 6. Two thousand respondents nationwide, from regions down to barangays, are selected for a national election. 7. Five hundred "like" in Facebook are used as basis for making a decision 8. Selected respondents for a study are those with acquired immune deficiency syndrome (AIDS). 9. Ten names of students were picked out from a box containing 1,000 names written in rolled papers 10. Respondents are chosen from a list

Gaussian State Spread
A measurement device which can be represented by a 1D quantum system (with canonical observables $X$ and $P$) 'is prepared in a Gaussian state with spread $s$'
$|\mathrm{\psi <!--\; \psi \; -->}⟩<!--\; ⟩\; -->=\frac{1}{({\mathrm{\pi <!--\; \pi \; -->}}^2{s}^2{)}^{1/4}}\int <!--\; \int \; -->\exp <!--\; \; -->[-<!--\; -\; -->\frac{x^2}{2s^2}]\mathrm{d}x|x⟩<!--\; ⟩\; -->$
Can somebody tell me what it means that its canonical variables are $X$ and $P$?

Example of identify risks, perform qualitative risk analysis and perform quantitative risk analysis

How is finite energy spread wholly in the infinite universe
We all know that energy is never lost, but it transforms into another form.
Doesn't that mean that energy is not unlimited? I mean, why is it that way if it was infinite?
However, if energy is spread throughout the whole world, how can something finite fully fill something infinite?
Does that mean that energy isn't finite? Or the universe isn't infinite? Or maybe there are places without any energy at all?
Of course, there is probably something stupid I'm missing, but an answer would hopefully fix that.
Note: sorry if it's a dumb question, I just heard of it and wasn't able to answer it, nor find it on the web.

What does alpha and beta signify in portfolio analysis?

Consider the following two datasets: $A=[5,23,8,12,4,21]$ and $B=[20,10,16,1,18,8,4]$. Please, select all correct options
a) The sample medians of the datasets are equal.
b) The sample means of the datasets are not equal
c) The sample means of the datasets are equal.
d) The ranges of the datasets are equal.
e) The sample medians of the datasets are not equal.

Why do wave packets spread out over time?
Why do wave functions spread out over time? Where in the math does quantum mechanics state this? As far as I've seen, the waves are not required to spread, and what does this mean if they do?

Can the standard deviation ever be negative?

What is the geometric mean of the pair of numbers 2 and 7?

What is an interquartile range?

How can regression analysis be used to formulate strategies?

A teacher wants to know if more than 15% of her students use online resources to complete their homework assignments instead of doing the homework independently. The teacher would like to carry out a test at the 0.05 significance level of
$H_0:p=0.40$
$H_a:p>0.40$
where p = the true proportion of students that use online resources to complete their homework assignments. One day after school, the teacher asked the 40 students studying in her classroom if they used online resources to complete their homework assignments or if they did their homework independently. Are the conditions to perform the significance test met?
No, the students do not represent a random sample and the Large Counts condition is not satisfied.
No, the students do not represent a random sample even though the Large Counts condition is satisfied.
No, the students represent a random sample, but the Large Counts condition is not satisfied.
Yes, the students represent a random sample and satisfy the Large Counts condition.

A tailor thinks that about $75\mathrm{\%<!--\; \%\; -->}$ of customers are satisfied with service. A random sample of $15$ customers, $8$ said they were satisfied. Calculate whether this is plausible at $5\mathrm{\%<!--\; \%\; -->}$ significance level.
I figured that $\mathrm{\mu <!--\; \mu \; -->}=0.6$, and $\stackrel{¯<!--\; ¯\; -->}{x}=8/15$, but I'm not sure how to get the variance. Can you assume satisfaction follows a Bernoulli distribution and calculate variance as $(0.75(1-<!--\; -\; -->0.75))/n$?