Get answers from academic experts to any study-related questions.
How would you make the multiplication of whole numbers a lesson? In the answer, use your knowledge of mathematics unit planning and lesson planning. Based on the basic concept of multiplying, the knowledge of number principles, and the understanding of multiplication and adding. Describe Multiplication as repeated addition, multiplication of...
How to construct one of the regular polygons with 6, 8, or 10 sides? Select one of the regular polygons with 6, 8, or 10 sides, and determine how to construct it using just a compass and a straight edge (you should not need to use any length measurements). The...
Descriptive statistics depict a set, while logical statistics take a sample of people for a specific model and generalize it to the entire group. Descriptive statistics are collected, for example, when local government elections take place. The inferential statistics are used to study the selected percentage of people from the...
The hypothesis is that eating before going to bed harms the period of night sleep. It is necessary to use an inferential method and study scientific articles and statistical data on how many people of the same age, gender, and health status experience negative consequences from eating before sleep. I...
To understand how much this information can be trusted, it is necessary to study the results of the conducted research. Some data summaries show how many people were interviewed, their data, and answers to the survey questions. I would clarify for what period people have studied tea and its effect...
An urgent question is whether it is worth getting vaccinated against Covid-19. I will study the statistics of the most reliable sources, for example, the New York Times. According to statistics from the New York Times, 60.4% of Americans aged 18 to 65 are fully vaccinated. Based on these data,...
I would agree with this statement since it represents one of the general rules of statistics. The idea behind it is that sampling error decreases as the sample size increases. It means that the census of the whole population would not be subject to the margin of error. This inverse...
RM-ANOVA is similar to one-way ANOVA, but unlike the second test, the first uses conjugate, linked groups. An example of this design could be a change in a value in a sample over time. In this case, the same people in the sample repeat actions, so the test is called...
One of the most popular tests is the LSD, which compares the difference between the means. In this test, pairwise comparisons are made between the means, and confidence intervals are constructed for them. Ultimately, this test measures the validity of all confidence intervals.
Post hoc tests are conducted after the ANOVA to determine the origin of the differences if they were found. So, if ANOVA shows differences between groups, post hoc shows precisely what the differences are. This is important because it allows for an in-depth analysis of differences and identifies variables that...
Dispersions can be heterogeneous, but for tests, it is necessary to assume that they conform to some principles, for example, that the distribution is normal. Violation of the assumptions can lead to errors in the conclusions and interpretations of the data. ANOVA tests are robust to a certain extent to...
ANOVA is a test used to detect a significant difference between three or more groups on an assessed parameter. Consequently, each group has some average, and an ANOVA test is conducted between groups to determine the significance of these differences. That is, how confident we can say that the averages...
The sampling distribution of a mean is a statistical method that might be employed for solving problems involving a considerably large number of samples. Statistical inference allows the researchers to calculate a statistic for each sample by repeatedly drawing samples from the selected population. Due to the variances in the...
A Z score is a standard score because it compares various variables through distribution standardization. This facilitates the establishment of how far a data point is from the mean. As such, scores above the mean possess positive z scores, and those below have negative z scores. However, since standard scores...
Wilcoxon Matched-Pairs Signed Rank Test is a traditional nonparametric test for the analysis of two paired samplings. It is used for the verification of the zero hypotheses and is quite similar to the paired t-test. According to Rietveld (2017), there are two main approaches to the WSR test, such as...
The teacher showed in the video What is a Triangle has an idea of how the development stages work, and it is noticeable that she has a lot of experience in teaching. The teacher adapts to the behavior of the students and selects new approaches or methods of teaching them....
Polynomials are described as algebraic expressions consisting of coefficients and indeterminate or variables combined by mathematical operations, which include multiplication, subtraction, addition, and division but not by a variable. The word polynomial consists of two Greek words: ‘poly,’ which means ‘many,’ and ‘nominal,’ which means ‘expressions or terms,’ and when...
The sum of -8 and 2 is negative because if you add a negative number with a larger value and a positive number with a smaller value, the sum remains negative. Conversely, when adding a positive number with a higher value and a negative number with a lower value, the...
Multiplication rules for numbers with the same sign. If the numbers are positive, then their product is found in the same way as natural numbers. To multiply two negative numbers, you need to put a plus sign and multiply the modules. This means that when multiplying numbers of the same...
The set of integers is the same, except that we include in set 0. Thus, integers are countable numbers plus 0. Once we have set up the count, we can start using operations, and the first ones we work with are addition and subtraction. Subtraction reveals negative numbers, which naturally...
Nominal Scale It is the scale where objects are defined based only on differences between them and as having or not having some quality. The example is the scale showing if the man is married or not married. Ordinal Scale The ordinal scale is the scale for evaluating the differences...
A mathematical phrase that groups numbers, variables, and operators to display the meaning of something is called an expression. An equation can be described as a statement with two expressions equal to each other. An expression is a piece of a sentence that represents a single numeric value. In contrast,...
The scales of measurement enable to manipulate data more precisely: to compare them, to see differences and similarities between them. Different scales are helpful for different purposes: the nominal scale is useful when the task shows the properties of the objects in the sample, while an interval or ratio scale...
Normal Distribution Known as the “bell curve,” it is symmetrical distribution, with values gradually rising to the mean value, which is the highest value as well, and gradually falling after it. Positive Distribution The distribution where data are skewed to the left (to the smaller value): its maximum is smaller...
Mean Depicted as μ, it is the average value of the sample of data. It is computed by the formula μ = (x1+x2+…+xn)/n. It is called an arithmetic mean: there are other mean values too, but the arithmetic mean is the most common. An example is an average mark on...
There are four basic arithmetic operations, notably addition, subtraction, multiplication, and division. With whole numbers that are also referred to as integers, those mean calculating “the number of individual items” based on adding them to one another or, contrariwise, dividing into groups. For example, in arithmetic operations with integer data,...
By definition, an equation is a mathematical statement whose sides balance each other or, in other words, describe the identical amounts. Meanwhile, if one of the sides undergoes any changes, for instance, multiplication, the number it expresses changes, and it cannot be equal to the other one anymore. In order...
In addition to assistance in solving mathematical problems, equations can serve the same in real life. One of the most frequent examples is apparently the calculation of calories. If a person knows how many calories their daily norm equals and how many they have already consumed, a simple equation will...
A polynomial is a mathematical expression that consists of several components, or terms, containing both numerical and literal symbols and connected by addition. An essential rule of a polynomial is that all its parts cannot be added, which means that the polynomial is already represented in the simplest form. Thus,...
Factoring is the process of splitting a complex mathematical expression into several simpler ones that are connected by multiplication, hence are factors. This method allows for simplifying the formulation of an equation, which, in turn, enables solving it faster. The essence lies in finding the highest common factor or factors...
An equation, both of whose sides are rational expressions — in other words, it only includes numbers, literal symbols, arithmetical operations, and integral powers — is also rational. Solving a mathematical problem frequently presupposes deriving, then solving a rational equation. The student must first assign X as the independent variable....
As the left side of a quadratic equation contains both the first and second power of the same variable, it is apparently possible to factor. The two resulting expressions need to equate to zero and solving; the solutions will be the roots of the initial one. Graphically, a quadratic equation...
One-way ANOVA is a statistical test that statisticians use in comparing averages of two or more groups. The test determines if the averages have major differences, which is attributable to their inherent differences in attributes. Normally, statisticians refer to unique attributes as treatments. Thus, statisticians use one-way ANOVA in determining...
Since a process entails a series of activities, focusing on the process by controlling each of the activities to provide the correct input would improve output. In contrast, focusing on the end-product does not improve output because it only gives a cumulative output of numerous activities, and thus, difficult to...
Types of non-experimental research designs: Descriptive: These designs explain a phenomenon. Examples include graphs, averages, and percentages. Relationships design: They describe the correlation between variables (two or more). Survey designs: They represent data gathering techniques essential in correlational and descriptive studies due to versatility, generalizability, and efficiency. Examples include cross-sectional...
The Likert Scale This is a scaling method for two extremities, which measure either negative or negative answers to a statement. Questionnaire This is a research tool that consists of a series of questions and other requirements with the aim of collecting information from participants. Checklist This is a listing...
Threats to the validity of qualitative research: Descriptive validity: This refers to what the researcher is unable to document while collecting information. Interpretation validity: The researcher requires capturing the study as interpreted by the person being researched. Researcher bias: Though every researcher is bound to be biased, the bias should...
Inferential statistics are used in an attempt to deduce from the sample data set what the population may think. For example, one may want to know whether second-year college males and females differ in statistics test scores.
An ANOVA F-test can tell about the extent of variation among population means. A large F-ratio implies that the variation of population means among groups is greater than the variation of population means within groups. In essence, ANOVA F-test can tell if the variability among population means due to treatment...
Statisticians use the Bonferroni method in adjusting the significance level for a set of p-values in multiple comparisons to change the probability of false rejection. The first step is to compute the p-values of each variable in the multiple comparisons. The second step is to select a significance threshold, such...
Internal validity regards how accurately an experiment is conducted, particularly when it evades mixing up more than one potential independent cause (variable) acting simultaneously. Internal validity is increased by avoiding confounding. The threats to internal validity are: History: the exact events that transpire between the 1st and 2nd measurement. Testing:...
In two-way ANOVA, the main effects indicate the unique effect of each independent variable on a dependent variable, controlling for other independent variables. Interactions are the combined effects of independent variables on the dependent variables. The interaction effect shows if independent variables act independently or synergistically to produce the apparent...
Quality control is a process that checks and ensures the quality of products or services meets the required standards. In nursing, quality control can be used in ensuring that nursing operations and procedures follow recommended procedures, guidelines, and standards set by regulatory bodies.
A capability is the potential of a process to meet required standards while control comprises activities performed to ensure that a process is predictable and consistent with required standards.
Mode refers to the value that appears most times in a set of numbers. When there is no number that has been reported, then there is no mode. Median is a value in the middle of a range of numbers when written in numerical order. Mean is obtained by adding...
Measurement validity is the extent to which a measurement instrument or approach is successful in quantifying or describing what it is. Construct validity: This is the extent to which a measure or a test examines the fundamental theoretical construct it is meant to measure. Convergent validity: This can be described...
Measurement reliability is the extent to which a measurement method can be relied on to secure dependable results when repeated. The results should be similar for subsequent measures. Inter-rater reliability: This is the extent of concordance among the raters. Test-retest reliability: This is achieved by giving the same test to...
Norm-referenced test pertains to normalized tests that are intended to contrast and grade test-takers in comparison to one another. For example, it would reflect how many fewer or more correct answers a test taker gave compared to other test takers. On the other hand, criterion-referenced tests outcomes are founded on...
Parametric and non-parametric statistical methods denote two general classifications of statistical procedures. Parametric tests are grounded in the assumptions about the distribution of the fundamental population, which provided the sample. The most widely spread parametric assumption implies that data are divided in an approximately normal manner. Non-parametric tests are not...
Measures of central tendency and dispersion attempt to describe data that is currently available in the SPSS dataset, with the most commonly used ones being the mean, median, and mode for measures of central tendency, and the standard deviation, variance, and range for measures of dispersion. Owing to the fact...
Probabilistic equivalence is a concept in experimental design methodology, which implies that the researcher is perfectly aware of the odds that he or she will find come across a pretest difference between the two groups under investigation. However, it does not necessarily mean that the two groups being studied will...
Independent variable is that element of experimental research, which is manipulated or changed by the research in order to cause changes in other elements being studied. Therefore, the independent variable is one of the core or major components of experimental research. It is the variable that is altered or manipulated...
Error variance is an important concept in experimental design methodology. It is used to describe the differences that exist between different variables in the study. In more specific terms, error variance is the variability that cannot be accounted for in experimental research using the systematic differences that the researcher is...
F-ratio is a statistical concept in experimental research design, which helps to assess whether variance in two different samples is equal. It is also used to determine the variance within groups of sample data as well as the variance between two groups of data. The F-ration is mostly applied in...
The p-value in research describes the probability that the H0 is true at a given level of significance. Thus, p = .05 means that, assuming a correct H0, the probability that the data (dependent variable) are significant is 0.05. If p < 0.05 (at 95% confidence), the H0 is rejected....
The NHST model is a statistic, such as a t-test, for determining whether a given variable causes the effect being tested. NHST tests often make certain assumptions. The NHST model (z-test and t-test) makes assumptions regarding the distribution of the tested variable. One such assumption relates to the normal distribution...
Inferential statistics allow a researcher to draw conclusions regarding the population based on the sample data. Thus, they enable the researcher to generalize the study’s findings to other populations. Inferential statistics determine the characteristics of the population based on the sample as well as the cause-and-effect relationship between the IV...
Prior probability is the estimated probability of the state of affairs before a practical survey is conducted to acquire relevant details. This is usually a conclusion based on past events. For instance, Peter passed the test (A) last year; therefore, the probability P (Pc) he will pass test C is...
Modal logic is an extension of formal logic that allows reasoning about certainties and possibilities. In comparison with classical logic, modal one considers that things may not always be as they are at that moment. For example, one may use modal logic by saying, “although the sun is usually yellow,...
De Morgan’s Laws are a pair of transformation logical rules and are an example of mathematical duality. They can be expressed as: the negation of a disjunction is the conjunction of the negations while the negation of a conjunction is the disjunction of the negations.
If a two-player strategy game is ultra-weak solved, it means determining the outcome (win, lose, or draw) if both players play perfectly. A weakly solved game implies an algorithm that means either win or draw, providing that the opponent can make all the possible moves. Solving a game in a...
The margin of error shows how accurate one expects the value of the unknown parameter to be. The margin of error of the given confidence interval is equal to ± 0.52 inches. This means that the value of ± 0.52 inches is the maximum amount by which the sample results...
In order to shorten the length of the confidence interval by half without changing the confidence level, the value of (σ / (number of samples0.5)) should be halved. Given that σ is the constant value, the number of samples needs to be increased, so that (new number of samples0.5) /...
Since z* is equal to 1.282 for the 80% confidence interval, the 80% confidence interval of the mean of the volume is 12.1 ± 1.282 × (0.24 / (36 0.5)) = 12.1 ± 0.05128. It can be stated that the calculated interval is smaller than the 90% confidence interval, with...
Given that income distribution in Utica is normal, it is possible to use Table A to estimate the probability that a single randomly chosen Utica household will have an income of less than $52,500. This is because the value of $52,500 can be standardized, and the cumulative proportion for the...
In order to use Table A, a standardized amount of money spent by shoppers should be calculated. For a shopper who spends $47 during one visit to Wainwright’s, this standardized amount of money equals z = (47 – 50) / 10 = -0.3. The cumulative proportion for z is 0.3821....
The Central Limit Theorem is a profound concept in statistics that makes statistically significant inferences about the general population based on samples. For example, a variable has a normal distribution (or any other type of distribution). One repeatedly takes samples from this general population and calculates the mean of each...
The name of the store and the following example of a survey were invented by the author. Kaufmann’s is a large department store that offers expensive clothing for high-income customers, both men and women. A limited collection of jewelry was launched for the first time, and a survey was designed...
In order to demonstrate the example when correlation does not imply causation, the article discussing the link between soft drinks and aggression in children was chosen. It is stated that heavy soda drinkers are much prone to violent behavior than other children. For this particular research, the intake of soft...
The chance of a hit in ideal conditions is 0.5. The player can either hit the ball and make a hit or miss with equal probability. In this sense, it is wrong to say that he must make a hit, but he can make a hit with a chance of...
The AVG parameter shows the success of the batting during a baseball game. Having discarded all other factors, the probability of hitting the ball with a bat is 0.5. From the law of large numbers, this parameter does not say anything about the likelihood of a successful strike during the...
In fact, according to Bernoulli’s law, the average result will tend to be 0.5, as the number of shots has increased, but the number of added goals and tails will not be the same. The intuitive answer that there will be 50 goals and 50 tails is wrong because it...
It is a mistake to assume that the probability of heads or tails falling out during a throw depends on previous results. Despite the last 108 throws, the likelihood of a head fall for a symmetrical coin will still be 0.5. But it is worth distinguishing the probability of a...
To find the median, the data should be arranged in order from least to greatest: 12, 55, 68, 72, 73, 77, 78, 84, 84, 85, 86, 86, 90, 92, 93, 93, 94, 94, 98, 100. Since there is an even number of items, the median is calculated as the arithmetical...
Pythagoras was another philosopher interested in discovering the nature of the substance. In his opinion, mathematics (more specifically numbers) is the answer to the question. Since numbers cannot be mistaken, understanding them would provide knowledge about the nature of the substance. He is widely known for his studies of geometry...
From the data given, the age of the students would be the variables since variables represent data that cannot be measured empirically. The cases would be the qualification entry requirements to the university since it is the subject matter of the analysis, and unlike the age of the students, it...
a. The average score of 385 points should be compared to the score of 400 points, considering that the tutor claims that their services will increase the average score of 350 by at least 50. z = ((x-μ)/√(σ2/N)) = ((385-400)/√(352/100)) = -4.285 The p-value for the z-score is 0.000009, which...
a. It is a good idea to choose stratified random sampling since it yields more accurate results, as compared to simple random sampling. Workers will be divided into groups by their position. Then, depending on the number of groups, a certain number of workers will be randomly chosen from each...
This is stratified sampling, as the researcher divided the general population into separate groups and randomly selected 10% from each group.
This is not a random sample since employees who did not attend the meeting did not have a chance to be selected. Instead, this is convenience sampling since subjects were chosen only because the manager could easily access them.
This sampling plan does not result in a random sample since individuals do not have an equal chance to be chosen. In fact, individuals that are at the end of the list may be not even reached if there are more than 2,500 people living in the city. Since the...
This is sample random sampling, as each student has an equal chance to be chosen.
Advantages: a lack of bias since all individuals are given an equal chance to be chosen and simplicity, as no additional procedures except for the randomization should be performed. Disadvantages: the need for a large data sample that would represent the total population and a lack of guarantee that conclusions...
I could think of one way of using a simple linear regression model to help me make better health choices. Some time ago, I stumbled upon a piece of research that showed that regular exercise correlated with better sleep quality. While it is now pretty established that physical activity improves...
Everyday use of the concept of confidence intervals that I can think of is buying clothes. It is common knowledge that sizing is often arbitrary and depends on the company. Sometimes, however, I think it is neither negligence nor malicious intent. People come in many shapes and sizes, and it...
Scholars emphasize the significance of the p-value in scientific research and statistics. P-value is the probability of receiving the result that is at least as extreme as the one mentioned in the sample data with the assumption that the null hypothesis is true. When the p-value is less than the...
Numbers, tables, and graphs are very useful when describing a single set of values or showing an association between two sets of values. A single set of values are used in everyday life. For instance, the teaching staff is fond of using single sets of values when evaluating the learners’...
One billion typically has 9 zeros and is written as 1,000,000,000. Explanation: When you need to solve a math problem with large numbers, it is important to know the differences between million, billion, and trillion. One million, however, is one thousand times less than a billion, meaning that it only...