Improve Your Understanding of College Level Statistics Problems

Find the x- and y-intercepts for both of the zero-net-growth isoclines, using the parameter values given below.
${\displaystyle r1=1}$
${\displaystyle к2=1}$
${\displaystyle s1,1=-0.02}$
${\displaystyle s1,2=-0.01}$
${\displaystyle s2,2=-0.02}$
${\displaystyle s2,1=-0.01}$
What are the general requirements for competing species to coexist? Based on the values for our two species, will the species coexist? How do you know?

Suppose that the n-th Riemann sum (with n sub-intervals of equal length), for some function f(x) on the intrval [0, 2], is $S_n=\frac{2}{n^2}\times \sum _{k=1}^{n}k.$
What is the value of ${\int }_0^{2}f(x)dx?$

The article “Stochastic Modeling for Pavement Warranty Cost Estimation” (J. of Constr. Engr. and Mgmnt., 2009: 352–359) proposes the following model for the distribution of Y = time to pavement failure. Let \(\displaystyle{X}_{{{1}}}\) be the time to failure due to rutting, and \(\displaystyle{X}_{{{2}}}\) be the time to failure due to transverse cracking, these two rvs are assumed independent. Then \(\displaystyle{Y}=\min{\left({X}_{{{1}}},{X}_{{{2}}}\right)}\). The probability of failure due to either one of these distress modes is assumed to be an increasing function of time t. After making certain distributional assumptions, the following form of the cdf for each mode is obtained: \(\displaystyle\Phi{\left[\frac{{{a}+{b}{t}}}{{\left({c}+{\left.{d}{t}\right.}+{e}{t}^{{{2}}}\right)}^{{\frac{{1}}{{2}}}}}\right]}\) where \(\Uparrow \Phi\) is the standard normal cdf. Values of the five parameters a, b, c, d, and e are -25.49, 1.15, 4.45, -1.78, and .171 for cracking and -21.27, .0325, .972, -.00028, and .00022 for rutting. Determine the probability of pavement failure within \(\displaystyle{t}={5}\) years and also \(\displaystyle{t}={10}\) years.

Give a complete and correct answer to the question asked what Posterior Probabilities?

Modeling ${\displaystyle C{O}_2}$ emissions
a) Use the data from 1960 and 1990 to find a linear function that models the ${\displaystyle C{O}_2}$
b) Use your linear function to predict the ${\displaystyle C{O}_2}$ emissions in 2005. Compare your prediction with the actual ${\displaystyle C{O}_2}$ emission in 2005

TWO GROUPS OR ONE? Situations comparing two proportions are described. In each case, determine whether the situation involves comparing proportions for two groups or comparing two proportions from the same group. State whether the methods of this section apply to the difference in proportions. (c) Compare the graduation rate (proportion to graduate) of students on an athletic scholarship to the graduation rate of students who are not on an athletic scholarship. This situation involves comparing: 1 group or 2 groups? Do the methods of this section apply to the difference in proportions? Yes or No

The expectation of the number of people getting their correct hats in the hat check problem, using linearity of expectations.
n persons receive n hats in a random fashion.
Formula used: By linearity of expectation function,
If $X_1,X_2,...,X_n$ are random variables, then
$E(X_1,+X_2+,...+X_n)=E(X_1)+E(X_2)+...+E(X_n)$ (2)

A population of values has a normal distribution with mean = 37.4 and standard deviation 77.4. If a random sample of size ${\displaystyle n=15}$ is selected,
Find the probability that a single randomly selected value is greater than 53.4. Round your answer to four decimals.
${\displaystyle P\left(X>53.4\right)=}$?

Consider the following research questions/study scenarios. For each study, discuss the most appropriate methods for describing the data (graphically and numerically). What statistical method would be most appropriate for addressing the research questions? Be sure to provide justification of the statistical method. Provide the appropriate regression model and statistical test when appropriate.
1.A study was performed to determine the differences in pain experienced by children with sickle cell disease (SCD) in inpatient and outpatient settings. Pain intensity (visual analog scale) was the primary outcome of interest, but potential confounders include age and physical activity.

How does the size of the cross-tabulation table impact the chi-square value.

The Kroger Company is one of the largest grocery retailers in the United States, with over 2000 grocery stores across the country. Kroger uses an online customer opinion questionnaire to obtain performance data about its products and services and learn about what motivates its customers (Kroger website, April 2012). In the survey, Kroger customers were asked if they would be willing to pay more for products that had each of the following four characteristics.
The four questions were: Would you pay more for:
products that have a brand name?
products that are environmentally friendly?
products that are organic?
products that have been recommended by others?
For each question, the customers had the option of responding Yes if they would pay more or No if they would not pay more.
a. Are the data collected by Kroger in this example categorical or quantitative?

Quantitative/Categorical Data Identify each of the following as quantitative data or categorical data.
a. The platelet counts in Data Set 1 “Body Data” in Appendix B
b. The cigarette brands in Data Set 13 “Cigarette Contents” in Appendix B
c. The colors of the M&M candies in Data Set 27 “M&M Weights” in Appendix B
d. The weights of the M&M candies in Data Set 27 “M&M Weights” in Appendix B

Answer the following true or false. If false, explain why. a. We can reduce $\alpha$ (alpha) by pushing the critical regions further into the tails of the distribution. b. A decrease in the probability of the type II error always results in an increase in the probability of the type I error, provided that the sample size n does not change. c. The p-value of a left-sided hypothesis test is always half of a two-sided hypothesis test.

Which possible statements about the chi-squared distribution are true?
a) The statistic $X^2$, that is used to estimate the variance $S^2$ of a random sample, has a Chi-squared distribution.
b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.
c) The Chi-squared distribution is used in hypothesis testing and estimation.
d) The Chi-squared distribution is a particular case of the Gamma distribution.
e)All of the above.

The numerical summary that is used for categorical data is a proportion.
Group of answer choices: True or False

A survey of 4826 randomly selected young adults (aged 19 to 25 ) asked, "What do you think are the chances you will have much more than a middle-class income at age 30? The two-way table summarizes the responses.
$\begin{array}{cccc}& \text{ Female }& \text{ Male }& \text{ Total }\\ \text{ Almost no chance }& 96& 98& 194\\ \text{ Some chance but probably not }& 426& 286& 712\\ \text{ A 50-50 chance }& 696& 720& 1416\\ \text{ A good chance }& 663& 758& 1421\\ \text{ Almost certain }& 486& 597& 1083\\ \text{ Total }& 2367& 2459& 4826\end{array}$
Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Given that the chosen student didnt

Identify the measures of center used for the data of company and union.
The number of sick days given to per employee and for the union. Measures of center:

Explain the variation in summary statistics by substracting the dataset into the percent value of 49.23.

To know:Distribution of the sum of multinomial random variables.
Covariance of multinomial random variables,
$COV(N_i,N_j)=-m{P}_i{P}_j,$

How can the sample covariance be used to estimate the covariance of random variables?