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The document discusses the difference between 95% confidence intervals and prediction intervals in regression analysis. Confidence intervals estimate the mean value of y for a given value of x, while prediction intervals give a range that a new individual y value is likely to fall within for that x value, accounting for variability in predicting individual values versus estimating means.

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You may need to use the appropriate appendx tabie or rechnology to answer this question.
Given are five observations collected in a regression thudy on two variables. Develop the 95%
confldence and prediction intervals when x= 8. (Round your answers to two dedimal piacesi)
Explein why these two intervals are difterent. The two intervais are different because there is
more varubility associated with predicting an individual value than there is with estimating a
mean value. The two intervals are different because you use a different critical value when
developing a confidence interval than when developing a prediction interval. The two intervals
are different because there is less variabaicy associated with predicting an individual value than
there is with estimating a mean value. The two intervals are offferent bectuse confidence
intervals are used to predict values of y for new observations corresponding to given values of x,
and prediction intervais give an asti the mean value of y for a given value of x.

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A simulated data analysis on the interval estimation for the

Alexander Decker

A simulated data analysis on the interval estimation for the

Alexander Decker

Answer the questions in one paragraph 4-5 sentences. · Why did the class collectively sign a blank check? Was this a wise decision; why or why not? we took a decision all the class without hesitation · What is something that I said individuals should always do; what is it; why wasn't it done this time? Which mitigation strategies were used; what other strategies could have been used/considered? individuals should always participate in one group and take one decision SAMPLING MEAN: DEFINITION: The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be WHAT IT IS USED FOR: It is also used to measure central tendency of the numbers in a database. It can also be said that it is nothing more than a balance point between the number and the low numbers. HOW TO CALCULATE IT: To calculate this, just add up all the numbers, then divide by how many numbers there are. Example: what is the mean of 2, 7, and 9? Add the numbers: 2 + 7 + 9 = 18 Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6 So the Mean is 6 SAMPLE VARIANCE: DEFINITION: The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number of items taken from a population. For example, if you are measuring American people’s weights, it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the weights of every person in the population. The solution is to take a sample of the population, say 1000 people, and use that sample size to estimate the actual weights of the whole population. WHAT IT IS USED FOR: The sample variance helps you to figure out the spread out in the data you have collected or are going to analyze. In statistical terminology, it can be defined as the average of the squared differences from the mean. HOW TO CALCULATE IT: Given below are steps of how a sample variance is calculated: · Determine the mean · Then for each number: subtract the Mean and square the result · Then work out the mean of those squared differences. To work out the mean, add up all the values then divide by the number of data points. First add up all the values from the previous step. But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ The handy Sigma Notation says to sum up as many terms as we want. · Next we need to divide by the number of data points, which is simply done by multiplying by "1/N": Statistically it can be stated by the following: · · This value is the variance EXAMPLE: Sam has 20 Rose Bushes. The number of flowers on each b.

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Section 7 Analyzing our Marketing Test, Survey Results and Other Metrics Using Confidence Intervals Rhonda Knehans Drake Associate Professor, New York University Data Analytics, Interpretation and Reporting copyright © 2013 2 • When we estimate population averages or percentages based on samples, a certain amount of error is present. • The amount of error present is a function mostly of your sample size. • The larger the sample, the less error in your estimates. • Today we will learn how to place bounds around our estimates obtained. • With such an interval, we will then be able to say with 90%, 95% or 99% confidence that the true population estimate will lie in these bounds. Introduction 3 The eight confidence interval formulas we will discuss are for the following situations: 1. Average or mean based on large samples 2. Average or mean based on small samples 3. Response rate or survey percent based on large samples 4. Response rate or survey percent based on small samples 5. Difference between 2 averages for large samples 6. Difference between 2 averages for small samples 7. Difference between 2 response rates for large samples 8. Difference between 2 response rates for small sample Confidence Intervals A-B Split Tests 4 1. Confidence Interval for Averages or Means Based on Large Samples (n ≥ 30) To calculate a confidence interval around a mean, the following information is required: – The sample mean x obtained from the test. – The sample standard deviation S obtained from the test. Many software packages, including Microsoft ExcelTM, can automatically calculate this value for you. (Review Section 3 for the standard deviation formula.) – The sample size n of the test. This is the number of observations used to calculate your mean. The sample size must be greater than or equal to 30 in size. – The desired confidence level: 90%, 95% or 99%. A confidence interval constructed around the mean will guarantee, with your specified level of confidence, the true mean will fall within those bounds. Sample Means (Large Sample) 5 • Once all information is known, you construct the confidence interval around the mean by adding and subtracting from the mean a multiple of your standard deviation associated with the sample mean. The “multiple” depends on your desired confidence level. • The formula for a confidence interval around the mean is calculated as follows: x  (Z )(S/n ) Where: • S is the standard deviation associated with the sample. • n is the sample size. • Z is equal to 1.645, 1.96 or 2.575 for a 90%, 95% or 99% confidence level Sample Means (Large Sample) 6 Example: Money magazine conducts a survey of 100 retirees across the US and asks them how much they have in their retirement fund. You obtain an average of $84.75 with a standard deviation of $18.75, both in thousands of doll.

Section 7 Analyzing our Marketing Test, Survey Results .docx

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Running head: HYPOTHESIS TEST 1 HYPOTHESIS TESTING 7 Project Phase 3 – Scenario 2 Author Note This paper is being submitted on Explain the 8 Steps in hypothesis testing. 1. State null hypothesis- this is the opposite of the expected results, the importance of stating the null hypothesis is because according to Karl Popper’s principle or Falsifiabilty, it not possible to exclusively confirm a hypothesis but it is possible to conclusively negate a hypothesis. 2. Alternative hypothesis- this is indication of what the experiment expects. It is stated as not all equal, because despite the fact that it is possible to have not all equal variables it is only one of the many chances. For instance, when comparing effect of infectious disease of the colour of urine the alternative hypothesis can state that disease 1 results in tinting of the colour of urine to yellow but disease 2, 3… and normal un-infected persons do not differ in the colour of urine. 3. Set α- this is the level of significance. This is the probability or chance of committing the ‘grievous’ error type one denoted by α There are two types of errors; Reality decision H0 is correct H0 in incorrect Accept H0 OK Type 2 error which is the β equal to possibility of type 2 error. H0 rejected Type 1 error α=possibility of type 1 error OK 4. Data collection- it’s important to use valid data collection techniques possibly for this case use observational or experimental methods 5. Stating and calculating the statistics for the study- this are the statistic values tested which include the mean, population, sample proportion and the difference in mean and sample proportions. mean 61.82 median 61.50 mode 69.50 Mid-range 58 range 41 variance 79.64 Standard deviation 8.3 6. Decide on the test to be used- there are basically two types of tests; one tailed and two tailed. The decision is reached depending on the spread of error; two tailed is used when error spread is on two extremes side while one tailed test is used when error is spread on one side in the distribution. 7. Create accept and reject regions- a critical F value is established, you can establish the study F value from the statistical tables it is also called the Fα. It represent the minimum value for the study test statistics which determine which values should be rejected. With the value of F you locate it in the F distribution which form the location for boundary for acceptance and rejection. 8. Standardize the test statistics to draw a conclusion- using step 5 and 6 you can make some inference on the study, but to make more specific conclusion computation of z-test will help decide on the whether to reject or accept the hypothesis. In such cases p-value lower then α, then null hypothesis H0 is conclusively negated and therefore should accept the alternative hypothesis HA. In testing a hypothesis using the above eight steps I prefer using critical value. This method include the coming up with the unlik ...

Running head HYPOTHESIS TEST 1HYPOTHESIS TESTING.docx

cowinhelen

Running head: PROJECT PHASE 4-INFECTIOUS DISEASES 1 PROJECT PHASE 4 – INFECTIOUS DISEASES 13 Project Phase 4 – Infectious Diseases Author Note This paper is being submitted on Project Phase 4 – Infectious Diseases Introduction: As a healthcare professional, you will work to improve and maintain the health of individuals, families, and communities in various settings. Basic statistical analysis can be used to gain an understanding of current problems. Understanding the current situation is the first step in discovering where an opportunity for improvement exists. This course project will assist you in applying basic statistical principles to a fictional scenario in order to impact the health and wellbeing of the clients being served. This assignment will be completed in phases throughout the quarter. As you gain additional knowledge through the didactic portion of this course, you will be able to apply your new knowledge to this project. You will receive formative feedback from your instructor on each submission. The final project will be due on week 5. Scenario: You are currently working at NCLEX Memorial Hospital in the Infectious Diseases Unit. Over the past few days, you have noticed an increase in patients admitted with a particular infectious disease. You believe that the ages of these patients play a critical role in the method used to treat the patients. You decide to speak to your manager and together you work to use statistical analysis to look more closely at the ages of these patients. You do some research and put together a spreadsheet of the data that contains the following information: · Client number · Infection Disease Status · Age of the patient You need the preliminary findings immediately so that you can start treating these patients. So, let’s get to work!!!! Background information on the Data: The data set consists of 60 patients that have the infectious disease with ages ranging from 35 years of age to 76 years of age for NCLEX Memorial Hospital. Remember this assignment will be completed over the duration of the course. To begin let’s learn what infectious disease is. Infectious diseases are caused by pathogenic microorganisms, which are bacteria, viruses, parasites or fungi; the diseases can be spread directly or indirectly, through one person to another (WHO, 2017). This scenario will aim to improve the quality of healthcare services that are provided to individuals, families, and communities at different levels of age. Therefore, the project utilized at NCLEX Memorial Hospital, over the past few days has seen a larger level of infectious disease occurrences. The data set composed was for sixty patients ranging in age from thirty-five to seventy-six. 1) a) Qualitative infectious: Disease b) Quantitative: Age 2) Age is a constant variable as it may take any value. 3) A variable is any quantity that can be measured and whose value differs through the Population and here we se ...

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Steps of hypothesis testing Select the appropriate test So far we’ve learned a couple variation on z- and t-tests See next slide for how to select State your research hypothesis and your null hypothesis State them in English Then in math Describe the NULL distribution Starting here is where you be a skeptic and assume the null is true! For one-sample tests, you will need to determine μ (For two-tailed tests, you don’t need to worry about μ) Compute the relevant standard error Determine your critical value(s) Keep in mind whether it is a directional or non-directional test Compute the test statistic Compare the test stat to the critical value(s) and make your decision When to use each test All of these tests require that the sampling distribution is normal Either because population is normal or, thanks to central limit theorem, sample size is very large All of these tests require that the measures be quantitative variables, that is interval/ratio (Not all quantitative variables are normal, BUT all normal variables are quantitative. So if someone tells you a variable is normal, you know it is also quantitative.) When to use each test, cont’d 1 Sample z-test Comparing one sample mean to a population mean And you do know σ (population SD) 2 sample z-test Comparing two sample means to each other And you do know σM1-M2 (standard error of difference of means) 1 sample t-test Comparing one sample mean to a population mean You only know s (sample SD) 2 sample t-test Comparing two sample means to each other You only know s1 and s2 (sample SDs) Dependent sample t-test You have two scores coming from each person, such as if you measured them before and after an experimental manipulation. Compute the differences between the two scores, then treat like a 1 sample t What is α? Put on your skeptic’s hat: you believe the null hypothesis is true But you’re willing to be convinced you’re wrong If the test statistic is sufficiently improbable, you will change your mind and decide the null hypothesis is false What is “sufficiently” improbable? When your test statistic is more extreme than your critical values Critical values are selected so that only a small fraction of the entire distribution is more extreme than the critical values This “small fraction” is called α Conventionally, α is usually set to .05, that is 5% Directionality of a test Is a test simply about whether there a difference, regardless of direction? If so, it is a non-directed, or undirected, or two-tailed test Your α must be evenly split between the two tails For the conventional α = .05, that means each tail should have .025 or 2.5% of the total distribution Is the test predicting one mean will be bigger than another? Or is it predicting one mean will be less than another? If so, it a directional, or directed, or one-tailed test Put all your α in a single tail Special note on one-tailed tests Step 3 of our procedure is a little awkward when we have one-tailed tests How do you descr.

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