How do you find the mean of 26, 25, 24,

Random variable X and Y have the joint PDF
$f_{XY}(x,y)=\{\begin{array}{l}c,x\ge 0,y\ge 0,(x^2+y)\le 1,\\ 0,otherwise\end{array}$
Find the marginal PDF ${\displaystyle f_X\left(x\right)}$.

A matched pairs design was used to compare test scores in a statistics course. Twenty-four students were chosen randomly from a large class. For each chosen student, their test 1 and test 2 scores were recorded. A 95% confidence interval for the difference in test scores was constructed, along with the corresponding 2-sided p-value was given as [−0.70,10.45], and the 2-sided p-value =0.084.
How does one determine whether or not this result is statistically significant at the 5% level of significance?
Also, if a 90 confidence interval was constructed instead of a 95% one, would it contain 0?
Would appreciate some clues.

What is the difference between probability distribution and sampling distribution?

Please specify the statistical test which would be most suitable for the situations below:
A possible association between smoking (yes/no) and snoring (yes/no) should be investigated.
An educating video is prepared for people about wearing a safety belt while driving. Their safety belt wearing habits were assessed before watching the video and re-assessed after a month of watching the educating video (n=17).

Decresing the sample size, while holding the confidence level and the variance the same, will do what to the length of wour confidence interval?

Suppose we observe the following random sample of size n = 117, sampled from a discrete distribution.
$\begin{array}{|cccccccc|}\hline \text{ Value }& 0& 1& 2& 3& 4& 5& 6\\ \text{ Count }& 32& 36& 21& 18& 6& 2& 2\\ \hline\end{array}$
We would like to test whether this data comes from a Poisson(${\displaystyle \lambda }$) distribution.
calculate the observed value of the appropriate Goodness of Fit test statistic, used to test the null hypothesis that the observed data is Poisson distributed.
Give answer to three decimal places. Compute the p-value of the observed test statistic you just computed. Give answer to three decimal places.

Here are summary statistics fro randomly selected weights of newborn girs:
${\displaystyle n=240,\bar{x}=26.1hg,s=6.3hg}$
Construct a confidence interval estimate of the mean. Use a ${\displaystyle 99\mathrm{\%}}$ confidence level. Are these results very different from the confidence interval
${\displaystyle 25.1hg<\mu <28.1hg}$
with only 13 sample values,
${\displaystyle \bar{x}=26.6hg}$ and ${\displaystyle s=1.8hg?}$
What is the confidence interval for the population mean ${\displaystyle \mu ?}$
Are the results between the two confidence intervals very different?
a) No, because each confidence interval contains the mean of the other confidence interval.
b) No, because the confidence interval limits are similar.
c) Yes, because the confidence interval limits are not similar.
d) Yes, because one confidence interval does not contain the mean of the other confidence interval.