Improve Your Understanding of College Level Statistics Problems

The pathogen Phytophthora capsici causes bell pepper plants to wilt and die. A research project was designed to study the effect of soil water content and the spread of the disease in fields of bell peppers. It is thought that too much water helps spread the disease. The fields were divided into rows and quadrants. The soil water content (percent of water by volume of soil) was determined for each plot. An important first step in such a research project is to give a statistical description of the data. Soil Water Content for Bell Pepper Study $$\begin{array}{cccccccccccccc}15& 14& 14& 14& 13& 12& 11& 11& 11& 11& 10& 11& 13& 16\\ 9& 15& 12& 9& 10& 7& 14& 13& 14& 8& 9& 8& 11& 13\\ 15& 12& 9& 10& 9& 9& 16& 16& 12& 10& 11& 11& 12& 15\\ 10& 10& 10& 11& 9\end{array}$$ If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation.

Construct 98% confidence intervals for the a) population variance and the b)population standard deviation ${\displaystyle \sigma }$ The number of hours of reserve capacity of 10 randomly selected automotive batteries. 1.71, 1.87, 1.58, 1.61, 1.78, 1.98, 1.36, 1.58, 1.47, 2.05, Assume the sample is taken from a normally distributed population.

Give the correct answer for this question: The Dunkers of Pennsylvania are members of a religious sect, about 50 of whom emigrated from Germany in the early 1700s.

Give a ffull answer its true or false: When an ANOVA comparing the means of 3 groups indicates that at least one group is different from the others, a common follow-up analysis to determine which group(s) is (are) different is pairwise two-sample t-tests each assessed using i) the pooled standard deviation when calculating the standard error for the difference in means and ii) a Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5%

Use a graphing calculator to graph the solution of the system of inequalities. Find the coordinates of all vertices, rounded to one decimal place.
$\{\begin{array}{l}y\ge x-3\\ y\ge -2x+6\\ y\le 8\end{array}$

Self-Driving Vehicle Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a self-driving vehicle Consider, X be the random variable that represents the number if adults who feel comfortable in a self-driving vehicle.
$\begin{array}{|ccccc|}\hline X& 0& 1& 2& 3\\ P(X)& 0.358& 0.439& 0.179& 0.024\\ \hline\end{array}$

Write the Different Ways of Measuring Angles The custom of measuring angles using degrees, with ${\displaystyle {360}^{\circ }}$ in a circle, dates back to the ancient
Babylonians, who used a number system based on groups of 60. Another system of measuring angles divides the circle into 400 units, called grads. In this system a right angle is 100 grad, so this fits in with our base 10 number system.
Write a short essay comparing the advantages and disadvantages of these two systems and the radian system of measuring angles. Which system do you prefer?
Why?

Distinguish the difference (purpose) between the two different types of chi-square
1.Chi-square test for independence (CTI)
2.Chi-square test for goodness of fit (CGF)
3.What type of variables are we using for a chi-square?

In a similar study using the same design (sample of $n=9$ participants), the individuals who wore the shirt produced an average estimate of $M=6.4$ with $SS=162$.
The average number who said they noticed was (population mean) 3.1. Calculate a One Sample t-test using a two-tailed test with ${\displaystyle \alpha =.05}$.

A population of values has a normal distribution with mean 18.6 and standard deviation 57. If a random sample of size ${\displaystyle n=25}$ is selected,
Find the probability that a sample of size ${\displaystyle n=25}$ is randomly selected with a mean greater than 17.5 round your answer to four decimal places.
P=?

1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation:

$\underline{\begin{array}{c}Gender\\ Affilation& Male& Female\\ Democrat& 300& 600\\ Republican& 500& 300\\ Other& 200& 100\end{array}}$

What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents:

$\underline{\begin{array}{c}SizeofCar\\ Gender& Small& Medium& lange& Total\\ Female& 58& 63& 17& 138\\ Male& 79& 61& 25& 165\\ Total& 137& 124& 42& 303\end{array}}$

the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ?

Here are summary stastistics for randomly selected weights of newborn girls: ${\displaystyle n=224,\bar{x}=28.3\text{hg},s=7.1\text{hg}}$. Construct a confidence interval estimate of mean. Use a 98% confidence level. Are these results very different from the confidence interval ${\displaystyle 26.5\text{hg}<\mu <30.7\text{hg}}$ with only 14 sample values, ${\displaystyle \bar{x}=28.6}$ hg, and ${\displaystyle s=2.9}$ hg? What is the confidence interval for the population mean ${\displaystyle \mu }$?

$27,2hg<\mu <29,4hg?$ (Round to one decimal place as needed).

Are the results between the two confidence intervals very different?

The following quadratic function in general form, ${\displaystyle S\left(t\right)=5.8t^2—81.2t+1200}$ models the number of luxury home sales, S(t), in a major Canadian urban area, according to statistical data gathered over a 12 year period. Luxury home sales are defined in this market as sales of properties worth over $3 Million (inflation adjusted). In this case, ${\displaystyle \left\{t\right\}=\left\{0\right\}\text{represents}2000\text{and}\left\{t\right\}=\left\{11\right\}}$represents 2011. Use a calculator to find the year when the smallest number of luxury home sales occurred. Without sketching the function, interpret the meaning of this function, on the given practical domain, in one well-expressed sentence.

Define the term stochastic models?

Find the median and quartiles for the data.

A population of values has a normal distribution with ${\displaystyle \mu =129.7}$ and ${\displaystyle \sigma =7.7}$. You intend to draw a random sample of size ${\displaystyle n=10}$.
Find the probability that a single randomly selected value is less than 130.9.
${\displaystyle P\left(X<130.9\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

For each of the following test, outline a research scenario and use any hypothetical data to show how the test is conducted.
i. One sample t-test
ii. Independent two-sample t-test
iii. Paired two-sample t-test
iv. Analysis of variance
v. Chi-square for goodness-of-fit test
vi. Chi-square test for independence

Nonparametric procedures can be applied to:
A)Categorical data
B)Data with an unknown distribution
C)Normally-distributed data
D)All of these responses are correct

How do frequency tables, relative frequencies, and histograms showing relative frequencies help us understand sampling distributions? They show each data point in the sampling distribution and how it relates to the overall distribution.They provide insight into the overall behavior of the population, therefore helping us understand the sampling distribution. They help us visualize the sampling distribution by using tables and graphs that approximately represent the sampling distribution.They help us visualize the sampling distribution by using tables and graphs that approximately represent the population distribution.

Critical Thinking How do frequency tables, relative frequencies, and histograms showing relative frequencies help us understand sampling distributions?