Improve Your Understanding of College Level Statistics Problems

A worker wanted to estimate the average annual living expenses for the residents of New Zealand. He randomly selected one of the suburbs and then collected the data for the annual living expenses for all residents.
Which of the sampling plans: simple random sampling, stratified random sampling or cluster sampling did the researcher use?
What are the advantage(s) and disadvantage(s) of the sampling plan used?

Which statement below is incorrect?
Select one:
A. In a survey study, we can never completely eliminate the random error, but it is possible to completely eliminate the systematic error.
B. Compared to the simple random sampling, it is easier to manipulate data with the systematic random sampling.
C. PACF and ACF can never have the same value.
D. If a time series has an upward trend over time, it cannot be stationary.

Tell me about this $p$-value in relatively simple but not too simple terms.
I've been reading many academic publications of late and come across it quite a few times without having a clear idea what it means. It's something about probability, isn't it? If it's less than, I believe, $0.05$, then it's, whatever it is, not a simple coincidence but a real correlation, right?

How do you find the average of 32, 53.3, 77.1, 100, 24, 48, 36, 40?

What is the mean, mode median and range of 11, 12, 13, 12, 14, 11, 12?

At the printing company I work for, we have different materials that we print on; part numbers for those materials are assigned based on the unique supplier, material type, and material widths (so the same supplier could send us two different widths of the same material type, and they'd get different part numbers). With each part number, our supplier sends us a statistical summary of their quality control data - how many samples were taken (n), the average thickness of the samples, and the standard deviation. For the most common parts, we might get a few hundred different averages, Ns, and standard deviations. I'm trying to group those summaries together. Since the sample size is so high, I'm fine averaging the average thicknesses for each part number; the numbers are closely grouped enough that it shouldn't be a significant difference. My question is, how do I summarize the standard deviation? The quality tests are standardized and the instruments used to measure the thickness are constantly calibrated, so I have no reason to think that the measurements would be inconsistent from one shipment to the next.

Surveys that combine one or more of simple random sampling, systematic random sampling, cluster sampling, and stratified sampling employ what is called sampling.

How does fire spread on a piece of paper?
If one lights the corner of a piece of paper with a match, the fire gradually spreads. What equation can be used to predict how the fire is going to spread spatially and temporally? At first, I thought thermodynamics would give answer to this question. But as far as I know, thermodynamics does not say anything about the dynamics of a system. So, how to tackle this question?

Does anyone know what the properties of t-values are?
As I know it's just the ration
$t=\frac{\stackrel{¯<!--\; ¯\; -->}{x}-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->}}{s/\sqrt{n}}$
which follows a t-distribution.
Used in mean-comparison tests and as a consequence also to check the significance of single independent variables in regression analysis. To generalize, t-values are used for hypothesis testing. Am I right with these properties?
Thanks!

Before using these variance estimates, what must we calculate?

How to find the median of 57, 68, 70, 85, 88, 88?

What type of information does a business risk analysis give?

The set of primitive recursive functions is [...] the smallest set containing the constant 0, the successor function, and projection functions, and closed under composition and primitive recursion.
My question is about the way composition, which does not seem very intuitive to me
If $f$ is a $k$-ary function and $g_0,\dots <!--\; \dots \; -->,g_{k-<!--\; -\; -->1}$ are $l$-ary functions on the natural numbers, the composition of $f$ with $g_0,\dots <!--\; \dots \; -->,g_{k-<!--\; -\; -->1}$ is the $l$-ary function $h$ defined by
$h(x_0,\dots <!--\; \dots \; -->,x_{l-<!--\; -\; -->1})=f(g_0(x_0,\dots <!--\; \dots \; -->,x_{l-<!--\; -\; -->1}),\dots <!--\; \dots \; -->,g_{k-<!--\; -\; -->1}(x_0,\dots <!--\; \dots \; -->,x_{l-<!--\; -\; -->1})).$
Is this just another way of stating composition as one may understand it in real analysis: that if we have
$g:<!--\; :\; -->{\mathbb{N}}^l\to <!--\; \to \; -->{\mathbb{N}}^k\text{and}f:<!--\; :\; -->{\mathbb{N}}^k\to <!--\; \to \; -->\mathbb{N},$
then we can define some composed function
$h:<!--\; :\; -->{\mathbb{N}}^l\to <!--\; \to \; -->\mathbb{N}?$
Or, would there be any "risk" at looking at the definition in this simplistic way?

Firstly, can we use the standard deviation to compare variability of two or more datasets? Why or why not?
Secondly, if the data is highly skewed, can we still rely on the kurtosis coefficient? Why or why not?

Which measure of central tendency is most resistant to sampling variation?

I have "solved" a question in mathematical statistics, but unfortunately received an incorrect answer and I would appreciate any help in understanding why my method did not work in this case. The question is as follows:
In city A, 500 randomly selected people were tested for antibodies to covid-19, which resulted in 110 giving positive results. In city B, a random sample of 500 people was also drawn, and here 91 had positive results. Can it be said that it is statistically certain that city A has a larger population share with antibodies than city B? (Justify your answer with an appropriate test. Use 5% significance level.)
I started by producing $P^{\ast <!--\; \ast \; -->}(A)=\frac{110}{500}=0.22$ and respectively $P^{\ast <!--\; \ast \; -->}(B)=\frac{91}{500}=0.182$.
Then I chose to continued with a one-sided hypothesis testing where I assumed that the data was binomially distributed according to $Bin(n=500,p)$, with$H_0:P=0.182\text{ and }{H}_1:>\mathrm{0.182.}$
And finally brought out the one-sided interval according to:$I_p={\mathrm{\lambda <!--\; \lambda \; -->}}_{\mathrm{\alpha <!--\; \alpha \; -->}}\sqrt{\frac{P^{\ast <!--\; \ast \; -->}(A)(1-<!--\; -\; -->P^{\ast <!--\; \ast \; -->}(A))}{n}}\Rightarrow <!--\; \Rightarrow \; -->[0.189,\mathrm{\infty <!--\; \infty \; -->}].$.And concluded that $H_0$ should be rejected since 0.182 is not included in the interval. But according to the results, $H_0$ should not be rejected and they have also used a different method than I did. Why is this method not applicable in my case?
Note: At first I thought that errors were because I only used α and not $\frac{\mathrm{\alpha <!--\; \alpha \; -->}}{2}$ in the calculation, however, even if I were to replace this, 0.182 is not in the interval.