Improve Your Understanding of College Level Statistics Problems

Let g be an element of a group G. If $|G|$ is finite and even, show that $g\ne 1$ in G exists such that $g^2=1$

1)What factors influence the correspondence between the binomial and normal distributions? 1.Twenty percent of individuals who seek psychotherapy will recover from their symptoms irrespective of whether they receive treatment. A research finds that a particular type of psychotherapy is successful with 30 out of 100 clients. Using an alpha level of 0.05 as a criterion, what should she conclude about the effectiveness of this psychotherapeutic approach? 2.How does the size of the data set help cut down on the size of the error terms in the approximation process?

The National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the World. A random sample of 50 cities gave the data on average high and low temperatures in January shown. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference

An experiment designed to study the relationship between hypertension and cigarette smoking yielded the following data.
$\begin{array}{|cccc|}\hline Tensionlevel& Non-smoker& Moderatesmoker& Heavysmoker\\ Hypertension& 20& 38& 28\\ Nohypertension& 50& 27& 18\\ \hline\end{array}$
Test the hypothesis that whether or not an individual has hypertension is independent of how much that person smokes.

CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies.
Find the probability that a single randomly selected value is less than 969 dollars.
${\displaystyle P\left(x<969\right)=P\left(x<969\right)=}$?

Write your answers as numbers accurate to 4 decimal places.

A population of values has a normal distribution with ${\displaystyle \mu =226.7\text{and}\sigma =59.8}$. If a random sample size of n=24 is selected.
Find the probability that a single randomly selected value is greater than 192.5.

Descibe in words the region of ${\mathbb{R}}^{\mathbb{3}}$ represented by the equation or inequality.
$y=-2$

The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer ("A Goodness of Fit Approach to the Class of Life Distributions with Unknown Age," Quality and Reliability Engr. Intl., $2012:761-766):115,181,255,418,441,461,516,739,743,789,807,865,924,983,1025,1062,1063,1165,1191,1222,1222,1251,1277,1290,1357,1369,1408,1455,1278,1519,1578,1578,1599,1603,1605,1696,1735,1799,1815,1852,1899,1925,1965.$
a) can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning. [Note: A normal probability plot of data exhibits a reasonably linear pattern.]
b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: mean $=1191.6,s=506.6$.]

To determine:Name the variables, specify for each variable whether it should be treated as categorical or quantitative and give the units for quantitative variables, if available. 

Explain the Chi – Square test.

A population of values has a normal distribution with mean 191.4 and standard deviation of 69.7. A random sample of size ${\displaystyle n=153}$ is drawn.
Find the probability that a sample of size ${\displaystyle n=153}$ is randomly selected with a mean between 188 and 206.6. Round your answer to four decimal places.
P=?

Explain whether the central limit theorem can be applied and assert that the sampling distributions of A and Bare approximately normal, if the sample sizes of A and Bare large.

Suppose that $X_1,X_2,...,X_{200}$ is a set of independent and identically distributed Gamma random variables with parameters $\alpha =4,\lambda =3$.
Describe the normal distribution that would correspond to the sum of those 200 random variables if the Central Limit Theorem holds.

Consider the function $f(x)=\sin x$ on th interval [0, 3]. Let P be a uniform partition of [0, 3] with 4 sub-intervals. Compute the left and right Riemann sum of f on the partition. Enter approximate values, rounded to three decimal places.

Means $=59.47444,SDS=12.91711,Min=23.599,Max=82.603$ AND Means $=67.00742,SDS=12.7302,Min=39.613,Max=82.603$ Means Based on your findings write a preliminary statistical report that comprises of the Methods, Results/Analysis and Conclusions sections. Include a comparison of the two distributions in (1) and (2) in terms of their central tendencies and variability. While your audience is one that lacks statistical expertise you are still expected to correctly interpret the data and statistical analyses, in a manner that is understandable to your audience. Be mindful to present an impartial report that distinguishes conclusive and inferential statements for the audience.

Explain which measure of center best describes a typical wage at this company:the mean or the median.

Explain the importance of the statement "Sampling distributions play a key role in the process of statistical interference" stated by the researchers Turner and Dabney.

Explain the meaning of the phrase " the sampling distribution of the sample statistic A"

Provide the formula for mean all symbols.