Inferential Statistics subject learning diary in which all the concepts are collected and all the tasks and exercises proposed during the course are carried out.
Presentation
This document collects the work history of the INTELLECTUAL Team during the application of Cooperative Learning in the subject of Inferential Statistics belonging to the Faculty of Administrative Sciences. The Journal is prepared collaboratively by all team members, and it is regularly reviewed and evaluated by the teacher. It includes the identity that the members give to the Team, a list of the students that make it up, the work done in each class, the achievements made and the individual and group self-evaluation of their performance.
Advancement of learning
Detail of the development of the topics planned in the syllabus. Main learning achieved in each session and identification of the learning needs that have remained to carry out the
search for relevant information.
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statistical-inferentialSession Topics Learned achievements Learning needs
1
Socialization of the syllable.
Full knowledge of the stipulated planning to carry out the inferential statistics matter, as well as the duties and rights that students are obliged to fulfill in the period.
Correctly operate the course planning, as well as appropriate collaborative learning in the course.
2
- Binomial Distribution: Counts the number of successes in a sequence of n independent Bernoulli trials, with a fixed probability p of success between trials.
- Poisson distribution: It expresses, from an average frequency of occurrence, the probability that a certain number of events will occur during a certain period of time.
- Z Distribution: The graph of its density function has a bell-shaped shape and is symmetric with respect to a certain statistical parameter.
Skill and greater emphasis when doing practice exercises in classes and homework.
Here is a series of 9 videos in which the concepts of the binomial distribution, the Poisson distribution and the Z distribution or normal distribution are explained through exercises, very important components of learning inferential statistics
3
Sampling and distribution of sampling
Sampling: The process of selecting a set of individuals from a population in order to study them and to characterize the total population.
In judgment sampling, personal knowledge and opinion are used to identify the elements of the population that should be included in the sample.
In probability sampling, all elements of the population have the opportunity to be chosen for the sample. Introducing four methods of random sampling:
-Simple random sampling.
-Systematic sampling.
-Stratified sampling.
-Bunch sampling.
in real situations.
Acquire and master information by actively applying what has been learned
4
Sampling distribution in detail Standard error Central limit theorem
It is what results from considering all the possible samples that can be taken from a population. Their study allows us to calculate the probability that we have, given a single sample, of approaching the population parameter. Using the sampling distribution, the error for a given sample size can be estimated.
Greater ease at the time of carrying out the exercises given by the teacher.
5
Relationship between sample size and standard error By decreasing the standard error, the
value of any sample mean will probably approach the value of the population mean, thus being able to estimate its value.
Furthermore, the accepted general rule says that if the sampling fraction is less than 0.05, it is not necessary to use the finite population multiplier. Understand and analyze
the statements of the different exercises carried out in class and homework for their respective solution.
6
Estimation Types of Estimation.
Estimate: An estimate is a specific observed value of a statistic.
• Criteria for a good estimator:
- Impartiality
- Efficiency
- Coherence
- Sufficiency
Estimation Types:
• Point estimation: it is a single number that is used to estimate an unknown population parameter.
• Interval estimation: it is a range of values that is used to estimate a population parameter.
Use the different formulas appropriately and correctly.
7
Confidence
Intervals Confidence Intervals:
Frequentist definition and interpretation.
• Confidence intervals for means and variances in normal populations: cases of one and two populations.
• Confidence intervals on large samples.
Determining the sample size
Understanding the topics in order to carry out the corresponding activities
8
Calculation of interval estimates of the mean from large samples
The estimation by confidence intervals consists of determining a possible range of values or interval, in which it can be specified with a certain probability that the value of a parameter is within those limits.
Analyze the parameters to better understand the topic covered.
9
First Partial Exam
10
Feedback from First Partial notes
11
Distribution or interval estimates with t distribution.
The t distribution was made by W. S Gosset in the early 20th century. Consequently, the t distribution is known as the Student t distribution or simply the Student distribution.
- Characteristics:
• Sample size must be less than 30 (n <30).
• Standard deviation must be unknown.
Do more exercises to understand the subject more.
12
Determination of the sample size in estimation. In all the analyzes done so far, we have used the symbol n instead of a specific number.
How large should the sample be? If it is very small, we may fail to achieve the objectives of our analysis; if it is too large, we waste resources taking the sample.
• Sample size to estimate an average.
• Sample size to estimate a proportion.
Understand the topic so that it is more effective when doing a job.
13
Single Sample Hypothesis Test.
We cannot accept or reject a hypothesis about a population parameter just by intuition rather, we need to learn how to objectively decide whether to accept or reject a hunch, based on the sample information.
• A hypothesis is a possible or impossible assumption of something to draw a consequence.
• A statistical hypothesis is a conjecture or assumption that is made regarding a specific population regarding a parameter of the population, which quantifies a characteristic of it. There is:
• Null hypothesis Ho.
• H1 alternative hypothesis.
Greater application of exercises oriented to the different scenarios that can be presented and, thus, obtain a greater understanding.
14
Portion Hypothesis Test.
Determine if the two independent samples were taken from two populations, which present the same proportion of elements with a certain characteristic. The test focuses on the relative difference (difference divided by the standard deviation of the sampling distribution) between the two sample proportions.
More analysis of the data is needed than the exercise provides to solve it correctly and understand it.
15
Hypothesis
testing of means when the population standard deviation is not known We learned that the size difference between large and small samples is important when the population standard deviation is not known and it is necessary to estimate it from the population standard deviation. the sample. If sample size n is 30 or less and is unknown, we must use the t distribution. The appropriate t-distribution has n-1 degrees of freedom.
Differentiate the sample size, given that the distribution t was used at 30 or less
16
Hypothesis test: two-sample
test The two-sample hypothesis test will take two random samples to determine if it comes from the same population or instead of equal populations, given that the populations are equal,
the mean between the two sample means are zero. If there are independent populations, they are equal to the sum of two individual variables. Therefore, the samples must be large enough so that the distribution of the sample means follows a normal distribution.
Contrast the dependent and independent samples in a practical way in order to avoid confusion when identifying them.
17
Tests for differences between means: small samples. Difference test between means with dependent samples.
Testing for Differences Between Means When sample sizes are small, two procedures are performed to test for differences between means. The first has to do with how we calculate the estimated standard error of the difference between two sample means. The second is testing small samples from a single mean. Basing our tests on the t distribution, rather than the normal distribution. Difference test between means with dependent samples. The use of dependent samples allows a more precise analysis to be carried out, because it allows controlling external factors. With dependent samples, the basic procedure adopted in all hypothesis tests is still followed.The only differences are that a different formula is used for the estimated standard error of the sample differences and that both samples need to be the same size.
Learn to recognize the data of each exercise in order to apply its respective formula. Recognize the formulas for dependent and independent samples.
18
Tests for differences between proportions: large samples
The general procedure to follow is very similar to what we did in the previous class with the two topics discussed, when we compared two means using independent samples: we standardized the difference between the two sample proportions and based our tests in the normal distribution. The only major difference will be in how we find an estimate for the standard error of the difference between the two sample proportions.
A better understanding of the null (HO) and alternative (H1) approach is needed.
19
Partial second exam and feedback of notes.
20
Absence from classes due to IESS teacher medical exams.
21
Non-attendance to classes due to Parties corresponding to the Cantonization of the Province.
22
Analysis of Variance
Allows the significance of the differences between more than two sample means; This is necessary because when you want to compare more than two means, it is incorrect to repeatedly use the contrast based on the Student's t-test. for two reasons: First, and since several hypothesis tests would be carried out simultaneously and independently, the probability of finding any significant one by chance would increase. In each contrast, the H0 is rejected if the t exceeds the critical level, for which, in the null hypothesis, there is a probability a. If m independent contrasts are performed, the probability that, in the null hypothesis, no statistic exceeds the
critical value is (1 - a) m, therefore, the probability that any one exceeds it is 1 - (1 - a) m, which for values of a close to 0 is approximately equal to m. The variance hypothesis can be tested using the Fisher distribution. Its significance level is 0.01 and 0.05.
Do more exercises so that the topic is better understood.
23
Chi-square
Chi-square is a hypothesis test that compares the observed distribution of the data with an expected distribution of the data. There are several types of chi-square tests: Chi-square goodness-of-fit test. The result of this comparison is compared with the Chi square distribution.
To be able to have a more concise class on the subject.
25
Simple Regression and Correlation Regression and correlation
analyzes will show us how to determine both the nature and the strength of a relationship between two variables. In this way, we will learn to forecast, with some precision, the value of an unknown variable based on previous observations of that and other variables. Types of Relationships The analyzes are based on the relationship or associations, between two (or more) variables. “The known variables are called Independent Variables; and the ones we are trying to predict are called dependent variables. "
• Direct line
• Inverse line
• Direct
curve
• Inverse curve • Inverse line with more dispersion
• No relation
Comprehension and analysis of the theory in order to understand the exercise resolution related to the topic.
26
Absence from classes since the Engineer had a pilot test programmed with the INEC
27
Simple Regression and Correlation
Advancement of Reforestation Project Planning.
Analysis of the formulas that will be used to solve the Simple Regression and Correlation exercises.
28
Estimation using the regression line The standard error of estimation Correlation analysis The coefficient of determination
• We will learn to calculate the regression line more precisely, using an equation that relates the two variables mathematically. Here, we will examine only linear relationships between two
variables; We will study the relationships between more than two variables.
• The standard error of the estimate, on the other hand, measures the variability, or dispersion, of the values observed around the regression line.
• Correlation analysis is the statistical tool that we can use to describe the degree to which one variable is linearly related to another.
The coefficient of determination is the main way in which we can measure the degree, or strength, of the association that exists between two variables, X and Y.
29
Complementing Regression Exercises with graphs
The regression line is derived from a sample and not from an entire population. As a result, we cannot expect the regression equation, Y = a + B * X (for the entire population), to be exactly the same as the equation estimated from sample observations, or Y = a + b * X. Even so, we can use the value of b, the slope that we calculate from a sample to test hypotheses regarding the value of B, the slope of the regression line for the entire population.
Analyze the composition of the formulas, as well as the procedure for carrying out the exercises.
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