Core statistics topics:
Sampling and distribution:
It involves the distribution of various samples from bulk-like population data. It mainly explains the distribution of frequencies or statistics. It can be measured with the help of variance or standard deviation. It mainly depends on the number of observations of the population, sample, and the choice of a random sample. With a large population size compared to the sample size, the sampling distribution has the same standard error.
Probability:
The probability of an event occurring measures the likelihood of that event. It provides a value between zero and one, depending upon the favorable outcome and sample space.
The value close to zero, classifies the less likelihood of the event, and the value close to one, shows the certainty of the event.
Random variables and probability distributions:
The random variable is a set of all possible outcomes in a sample space, represented by some number. In other words, it is a function that represents each point on a sample space by a number. For example, the following table represents the outcome of tossing a coin twice.
Sample Space (S) | TH | TT | HT | HH |
Random Variable (X) | 1 | 2 | 1 | 0 |
Let X represent the number of tails that can come up. We can represent that by assigning a number to each sample point. We can see, the number of tails is randomly changing, Thus X is a random variable.
Nonparametric statistical techniques:
The nonparametric test is used when the population size is small and has an unknown distribution.
In this type of statistical technique, the population data analyzed does not require to meet the population parameter.
However, this technique has some advantages, but this is less effective to analyze the relationship between the variable, if one exists.
Hypothesis testing:
Hypothesis testing is an analysis performed on the sample data. It is used to check the hypothesis regarding a population.
In order to test the idea regarding population parameters, we begin by setting a null hypothesis, and an alternate hypothesis. And, we try to reject the null hypothesis.
Statistical analysis:
Statistical analysis refers to techniques of extracting useful pieces of information, such as trends, patterns, etc, from the collected data.
The collected data is represented using statistics, in a way that makes it easy to visualize the information.
For example, the analyzed data could be represented by a Pie Chart. It makes more sense out of given data.
Tree diagrams:
The tree diagram is used to represent the sample space data of an event. It is used for a relatively small set of data.
It shows the probability of an event on the branch, and outcome at the end of the branch.
For example, the probability of an event A tossing a coin twice could be represented as:
Outliers:
An outlier is a variable, or data point, which is either very below from the mean of the data, or very far from the mean.
In other words, the outlier lies outside the concentrated data points. The outliers increase the standard deviation.
Bayes’ Theorem:
Bayes’ theorem gives a formula for determining conditional probability. It can calculate the probability of an event, based on certain previous likelihood of the event.
Where:
- Probability of event A.
- Probability of event B.
- The independent probability of A given B.
- The independent probability of B given A.
Sample Statistics Homework Help – Questions and Answers
Q. If m things are distributed among ‘a’ men and ‘b’ women, find the chance that the number of things received by men is odd.
Sol. Probability that the man gets a things = a/(a+b) = p
Probability that the woman gets a things = b/(a+b) = q
Probability that r things are received by men = P(r) = .^m C_r p^r.q^(m-r)
Since men are to receive odd number of things i.e. 1 or 3 or 5 or … … …
So required probability is
=P(1)+P(3)+P(5)+⋯………
=^m C_1 p.q^(m-1)+.^m C_3 p^3.q^(m-3)+.^m C_5 p^5.q^(m-5)+⋯………
=1/2{(p+q)^m-(p-q)^m}
=1/2 {1-((b-a)/(b+a))^m }
Q. Find correlation coefficient between X and Y if covariance of X and Y is 100, variance of X is 10000, and variance of Y is 4.
Sol. Given,
Cov(X,Y)=100
Variance of X = 10000 ⇒ σ_x^2=10000
⇒σ_x=100
Variance of Y = 4 ⇒σ_y^2=4
⇒σ_y=2
So, r= Cov(X,Y)/(σ_x 〖 σ〗_y )
r= 100/(100×2)
r= 1/2
r=0.5
Q. Pumpkins were grown under two experimental conditions. Two random sample of 11 and 9 pumpkins show the sample standard deviations of their weights as 0.8 and 0.5 respectively. Assuming that the weight distributions are normal, test the hypothesis that the true variance are equal, against the alternative that they are not equal, at the 10% level
Sol. We want to test Null Hypothesis, H_0:σ_X^2=σ_Y^2 against the
Alternative Hypothesis, H_1:σ_X^2≠σ_Y^2 ( Two-Tailed)
We are given : n_1=11, n_2=9
s_X=0.8, S_Y=0.5
Under the null hypothesis we have statistics as
F= (s_X^( 2))/(s_Y^( 2) ) , follows F distribution with (n_1-1,n_2-1) degree of freedom
Also, n_1 s_X^( 2)=(n_1-1) S_X^( 2)
So, S_X^( 2)= n_1/(n_1-1) s_X^( 2 )= 11/10 ×(0.8)^2=0.704
Similarly, S_Y^( 2)=0.28125
So, F= 0.704/0.28125 =2.5
The significant values of F for the two-tailed test at the level of significance α=0.10 are:
F>F_10,8 (α/2) =F_10,8 (0.05)
F<F_10,8 (1-α/2) =F_10,8 (0.95)
We are given the tabulated values
P(F_10,8≥3.35)=0.05⇒F_10,8 (0.05)=3.35
P(F_8,10≥3.07)=0.05⇒P (1/F_8,10 ≤1/3.07) =0.05
⇒P(F_10,8≤0.326)=0.05⇒P(F_10,8≥0.326)=0.95
Hence from above values the critical values for testing null hypothesis against the alternative hypothesis at the level of significance α=0.10 are given by:
F>3.35 and F<0.326=0.33
since the calculated value of F=2.5 lies between 0.33 and 3.35, it is not significant and hence null hypothesis of equality of population variances may be accepted at level of significance α=0.10
Hire Best Statistics Homework Helpers Now!
Get Timely Solutions to Statistics Homework and Assignment Question!
We assist parents, looking for solutions for complex statistics homework problems for their children.
Our seasoned Statisticians, with years of experience in the field of academics, have helped thousands of students in this subject. Not only do they help your child in solving complex problems, but the detailed homework solutions provided by our stats tutors equip your child with the confidence needed to solve their stat homework on your own the next time.
This way we set them for long-term success and help them improve their grades in stats class and stop saying - Mom can you do my statistics homework?
If you are a high school or college level student looking for statistics homework help online or struggling to do your statistics homework, we have also got you covered.
Statistics written help is available to you 24*7 at TutorEye. Our experts are here round the clock, day and night, and can help you in finding high-quality answers for a statistics project, complete your stats dissertation or thesis on time. Avail writing assistance for better conceptual clarity to even meet a term paper or coursework deadline. Our solutions will give you step-by-step explanations of your statistics problems and detailed instructions on how to solve your textbook questions.
Writing assistance works best for those students who need a map or an instruction booklet that can help them figure out complex problems.
To get statistics to help online, join our platform and get matched to a tutor of your choice. Getting statistics homework help online is now so simple! Our tutors go through a rigorous screening process and have years of experience in teaching students worldwide.
Upgrade your knowledge in statistics with the most trusted statistics homework solvers and gain mastery in representing data in diagrammatic and tabular form. Learn about principal component analysis and derive valid inferences.
Understand and learn random variables to predict uncertain outcomes. With the help of our tutors understand the use of various statistical concepts, techniques, and methods. Quality statistics assignments and homework help are just a click away.
We will help you submit flawless work and well-researched term papers with proper statistical inferences.
To know all about testing hypotheses, sampling, and distributions make us your study partner today.
What is the process to get guidance from an expert statistics homework helper?
Availing online statistics homework help from a seasoned tutor is so easy now. On our platform, we simplify the process for you.
Step 1: Fill out your request details on our homework help form
Step 2: Choose a proposal that meets your submission timelines and suits your pocket. Go ahead and hire the tutor by reaching an agreement on the budget.
Step 3: Release payment from escrow once you review your assignment.
To avoid any discrepancy we follow a Money Refund policy. Upgrade with the best homework solvers today!
Frequently Asked Questions about Statistics Homework Help:
What is statistics?
Statistics is an interdisciplinary field concerned with collecting data, analyzing, interpreting and presenting empirical facts by carrying out qualitative and quantitative research.
You will learn how to arrive at inference and learn techniques like sampling to summarize results. There are two types of Statistics: Descriptive and Inferential.
In the study of descriptive statistics, a given data set is summarized whereas in inferential statistics, you get to make predictions from a given sample or size of populations.
By studying Statistics, you can make intelligent assumptions and draw conclusions by analyzing data in any field.
What does n mean in statistics?
The symbol 'n’ stands for the total number of observations or individuals in the sample. It is also referred to as sample size.
What is r in statistics?
The symbol ‘r’ in Statistics refers to correlation coefficient. The values for it range from ‘-1’ to ‘+1’ and if it is ‘0’ it means there is no relationship between the variables. The variables are believed to be related if it is closer to +1 or -1.
What is mu in statistics?
The greek letter “mu” stands for population mean.
What is N in statistics?
In statistics, N refers to population size.
What is a parameter in statistics?
In a statistical analysis, parameter stands for characteristics that are used to define a given population. Hence, it is a useful component to carry out an analysis as it points to a specific characteristic of an entire population.
What is “s” in statistics?
The letter ‘s’ stands for standard deviation of a sample.
What is "p" in statistics?
The p value in statistics helps you determine whether you should accept or reject a null hypothesis. The smaller the p-value, the stronger the evidence to go ahead and reject the null hypothesis.The value of ‘p’ is used as evidence against a null hypothesis.
What is descriptive statistics?
Descriptive Statistics simply describes what the data shows. In other words, it describes the data and summarizes it. It is a simple summary about the given sample.
What is inferential statistics?
Inferential data stands for making inferences or drawing conclusions that extend beyond immediate data. It takes data from the sample and makes predictions about the entire population.
What is sigma in statistics?
The greek letter sigma denoted as “σ” stands for the standard deviation of a population.
What is power in statistics?
To put it simply, power is a probability to not make a Type 2 error and it increases when the sample size is increased. To detect a false null hypothesis, power must be close to 1 and if it is lower than 0.8, is considered too low to carry out research. Therefore, it is an important concept to understand in Statistics.
What is r squared in statistics?
In Statistics, R squared is also known as the coefficient of determination.It determines how close the data is to the fitted regression line. It is always between 0-100%. In most cases the larger the R squared the better the regression model fits your observation.