Improve Your Understanding of College Level Statistics Problems

State the differences and similarities between simple random sampling procedure and systematic sampling procedure.

How does probability relate to statistical significance?

In various applications where we are dealing with electromagnetic or acoustic waves, such as medical imaging, we use the space $L^2$ or the related Sobolev space $W^{1,2}$. I have never seen a reason given for this. Does anyone know why these spaces are preferred over say $L^1$ spaces?

Is age a discrete or continuous variable? Why?

A manufacturer of sports equipment has developed a new synthetic fighting line, which he claims has a mean breaking strength of 15 pounds with a standard deviation of 0.5 pounds.
Test the hypothesis that $\mathrm{\mu <!--\; \mu \; -->}$ = 15 pounds against the alternative that $\mathrm{\mu <!--\; \mu \; -->}$ + 15 pounds, if a random sample of 50 lines is tested and found to have a mean breaking strength of 14.8 pounds.
Use a 0.01 level of significance.

Joachim, a third student, noted that the confidence interval in part (a) gives plausible values of the parameter as an interval between two values. He suggested that they develop a one-sided confidence interval because they were only concerned with whether the number 6 was landing face up more often than expected, not less often. The one sided-interval will determine a value L such that all plausible values of p are greater than L. The formula for L is .
(i) Determine the values of z∗ needed to create the one-sided 95 percent confidence interval. Then calculate the value of L.
(ii) Do the results of Joachim’s one-sided confidence interval agree with results of Aurelia’s significance test in part (b)?
Explain your reasoning.

To test for the significance of the phi correlation, one must use the ______________ distribution.
Group of answer choices:
1.t
2. Chi-square
3. z
4. F

How do you write down 5 numbers where the mean is 7 and the median and mode are 6?

I passed the real analysis course at my college and now, after 3 years, im not that good anymore at integrating, solving big complicated limits etc. But I still remember the concepts behind them. Now, since I'm trying to self-study some topics that I'm not familiar with (topology, galois theory etc), as an aspiring engineer, I was wondering if I shouldn't move to the next topic until I'm very good at doing every exercise (“calculate the integral of” “calculate the limit of” etc) with the risk of one day forgetting almost everything or if i should focus more on understanding the concepts and use a computer for the calculations.

How do you find the average of percentages?

In each of Exercises, we have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.
$x=20,s=4,n=32,HO:\mathrm{\mu <!--\; \mu \; -->}=22,Ha:\mathrm{\mu <!--\; \mu \; -->}<22$

I've analysed newspapers by counting the language distributions of the articles.
The results look like that:
$\overline{)\begin{array}{ccc}\text{Day1}& \text{Day2}& \text{Day3}\\ Economy& Economy& Economy\\ \text{Language 1: }0.35& 0.30& 0.90\\ \text{Language 2: }0.11& 0.10& 0.00\\ \text{Language 3: }0.54& 0.60& 0.10\\ \text{Sport}& \text{Sport}& \text{Sport}\\ \text{Language 1: }0.40& 0.30& 1.00\\ \text{Language 2: }0.20& 0.20& 0.00\\ \text{Language 3: }0.40& 0.50& 0.00\end{array}}$
I've have already posted another question on that topic (Remove statistical outliers), but here comes my second problem. First of all, I want to remove all statistical outliers from data (e.g. day 3), to make it "clean" (see my other question (other post). After that, I want to terminate which changes in my data are just "noise" and witch are significant changes. But I'm not sure how to do it.
I was thinking of the following approach:
I could calculate the standard deviation (like in my other post) and treat every value outside of it as a "significant change". But I think this will cause a mistake if all my values are slightly increasing or decreasing.
Is there any mathematical technique to find the significant changes in my data?
Thanks in advance.

The log return X on a certain stock investment is an N(μ,σ2) random variable.
A financial analyst has claimed that the volatility σ of the log return on this stock is less than 3 units. A random sample of 11 returns on this stock gave an estimated variance of the log-returns as s2=16.
Assess the analyst's claim by using a significance test at level
α=0.05 to test
H0:σ2≤9 against H1:σ2>9.
Find a two-sided 95% confidence interval for σ2.

A disease effects 1/1000 newborns and shortly after birth a baby is screened for this disease using a cheap test that has a 2% false positive rate (the test has no false negatives). If the baby tests positive, what is the chance it has the disease?
I've got $P(\text{disease | positive})=\frac{P(d^p)}{P(p)}=\frac{(1/1000)}{(1/1000+2/100\ast <!--\; \ast \; -->999/1000)}=\frac{1}{(20+49/50)}$
Is this right?

Identify the type of sampling method used by the researcher in each situation: simple random sampling, systematic sampling, stratified sampling, or cluster sampling.
1. A researcher interviewed all the nurses in each of the 5 randomly selected private hospitals in Northern Mindanao.
2. A statistician selected a sample of ? = 500 high school students from a private school with 2,500 students. He randomly selected the students from each grade level.
3. A Statistics student did a research on the time spent by Grade 11 and 12 students in playing mobile legends. He randomly selected his subjects by using the Table of Random Numbers.
4. A teacher conducted a study in her school to determine who were better in mathematics: the males or the females.

Oil spreading over water
The book says that oil spreads over water due to the greater surface tension of water as compared to oil, so the comparatively stronger water film stretches the oil surface and makes it spread... But if this is the case, doesn't that mean that the oil layer will go on spreading indefinitely(even if it gets one molecule thick)until it covers the whole surface, because at any point the surface tension of water is still greater than oil.... But this does not happen, oil spreads only until it makes a particular contact angle with the water surface.
So is the explanation given in the book a bit faulty or am I getting the whole thing wrong? Someone please help...

Identify the sampling scheme applied in each of the given situations. Write the complete name of sampling procedure. Explain your answer in at most 5 sentences.
1. One hundred children chosen at random by lottery method from the list of pupils enrolled in the barangay Day Care Center will form a sample for the study of occurrence of malnutrition among pre-school children in a certain barangay.
2. Students are grouped according to year level. Ten representative from each year level were chosen at random using lottery method to answer a survey on the use of Blended Learning Approach.

What is the geometric mean of the pair of numbers 576 and 4?