1. Illustrate point and interval estimations.
2. Distinguish between point and interval estimation.
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Chapter 5 part1- The Sampling Distribution of a Sample Meannszakir
Β
Mathematics, Statistics, Population Distribution vs. Sampling Distribution, The Mean and Standard Deviation of the Sample Mean, Sampling Distribution of a Sample Mean, Central Limit Theorem
T test, Studentβs t Test, Key Takeaways, Uses of t-test / Application , Type of t-test, Type of t-test Cont.., One-tailed or two-tailed t-test, Which t-test to Use, t-test Formula, The t-score, Understanding P-values, Degrees of Freedom, How is the t-distribution table used, Example, Example Cont.., Different t-test Formulae, Different t-test Formulae Cont.., Reference.
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Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.1: Estimating a Population Proportion
Chapter 5 part1- The Sampling Distribution of a Sample Meannszakir
Β
Mathematics, Statistics, Population Distribution vs. Sampling Distribution, The Mean and Standard Deviation of the Sample Mean, Sampling Distribution of a Sample Mean, Central Limit Theorem
T test, Studentβs t Test, Key Takeaways, Uses of t-test / Application , Type of t-test, Type of t-test Cont.., One-tailed or two-tailed t-test, Which t-test to Use, t-test Formula, The t-score, Understanding P-values, Degrees of Freedom, How is the t-distribution table used, Example, Example Cont.., Different t-test Formulae, Different t-test Formulae Cont.., Reference.
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Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.1: Estimating a Population Proportion
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.1: Estimating a Population Proportion
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.2: Estimating a Population Mean
Running head COURSE PROJECT NCLEX Memorial Hospital .docxsusanschei
Β
Running head: COURSE PROJECT: NCLEX Memorial Hospital 1
COURSE PROJECT: NCLEX Memorial Hospital 10
Introduction
This project aims to facilitate the improvement of the quality of healthcare services provided to individuals, families and communities at various age levels. Hence, this project used NCLEX Memorial Hospital, where over the past few days there has been a high level of infectious diseases. The dataset collected is from 60 patients whose age range is 35 to 76.
Classification of Variables
The quantitative variable is age. The qualitative variable is infectious diseases. Age is also a continuous variable as it can take on any value. A variable is any quantity that can be measured and whose value varies through the population and here the level of measurement is age, which we shall label a nominal measurement as numbers are used to classify the data.
The Measures of Center and the Measures of Variation
Themeasures of center are some of the most important descriptive statistics one might extrapolate. It helps give us an idea of what the "most" common, normal, or representative answers might be. Essentially, by getting an average, what you are really doing is calculating the "middle" of any group of observations. There are three measures of center that are most often used: Mean, Median and Mode. (NEDARC)
While measures of central tendency are used to estimate "normal" values of a dataset, measures of variation/dispersion are important for describing the spread of the data, or its variation around a central value. Two distinct samples may have the same mean or median, but completely different levels of variability, or vice versa. A proper description of a set of data should include both of these characteristics. There are various methods that can be used to measure the dispersion of a dataset, each with its own set of advantages and disadvantages. (Climate Data Library)
The Measures of Center and the Measures of Variation Calculations
Column1
Mean
61.81667
Standard Error
1.152127
Median
61.5
Mode
69
Standard Deviation
8.924337
Sample Variance
79.64379
Midrange
58.5
Range
41
Conclusion
By looking at the dataset we find that patients after the age of 50 and most likely 60 to be the most affected by infection diseases. Hence, there should be a prevention plan in place to reduce the number of infected or most likely to be affected by various viruses.
Course Project Phase 2
Introduction
The data in the accompanying spreadsheet records the ages of sixty (60) patients at NCLEX Memorial Hospital who, upon admission, were found to be suffering from ...
Standard Error & Confidence Intervals.pptxhanyiasimple
Β
Certainly! Let's delve into the concept of **standard error**.
## What Is Standard Error?
The **standard error (SE)** is a statistical measure that quantifies the **variability** between a sample statistic (such as the mean) and the corresponding population parameter. Specifically, it estimates how much the sample mean would **vary** if we were to repeat the study using **new samples** from the same population. Here are the key points:
1. **Purpose**: Standard error helps us understand how well our **sample data** represents the entire population. Even with **probability sampling**, where elements are randomly selected, some **sampling error** remains. Calculating the standard error allows us to estimate the representativeness of our sample and draw valid conclusions.
2. **High vs. Low Standard Error**:
- **High Standard Error**: Indicates that sample means are **widely spread** around the population mean. In other words, the sample may not closely represent the population.
- **Low Standard Error**: Suggests that sample means are **closely distributed** around the population mean, indicating that the sample is representative of the population.
3. **Decreasing Standard Error**:
- To decrease the standard error, **increase the sample size**. Using a large, random sample minimizes **sampling bias** and provides a more accurate estimate of the population parameter.
## Standard Error vs. Standard Deviation
- **Standard Deviation (SD)**: Describes variability **within a single sample**. It can be calculated directly from sample data.
- **Standard Error (SE)**: Estimates variability across **multiple samples** from the same population. It is an **inferential statistic** that can only be estimated (unless the true population parameter is known).
### Example:
Suppose we have a random sample of 200 students, and we calculate the mean math SAT score to be 550. In this case:
- **Sample**: The 200 students
- **Population**: All test takers in the region
The standard error helps us understand how well this sample represents the entire population's math SAT scores.
Remember, the standard error is crucial for making valid statistical inferences. By understanding it, researchers can confidently draw conclusions based on sample data. ππ
If you need further clarification or have additional questions, feel free to ask! π
---
I've provided a concise explanation of standard error, emphasizing its importance in statistical analysis. If you'd like more details or specific examples, feel free to ask! ΒΉΒ²Β³β΄
Source: Conversation with Copilot, 5/31/2024
(1) What Is Standard Error? | How to Calculate (Guide with Examples) - Scribbr. https://www.scribbr.com/statistics/standard-error/.
(2) Standard Error (SE) Definition: Standard Deviation in ... - Investopedia. https://www.investopedia.com/terms/s/standard-error.asp.
(3) Standard error Definition & Meaning - Merriam-Webster. https://www.merriam-webster.com/dictionary/standard%20error.
(4) Standard err
1. Illustrate the t-distribution.
2. Construct the t-distribution.
3. Identify regions under the t-distribution corresponding to different values.
4. Identify percentiles using the t-table.
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Distinguish between Parameter and Statistic.
Calculate sample variance and sample standard deviation.
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Know the types of Random Sampling method and how it is being used.
Simple random sampling
Systematic sampling
Stratified Sampling
Cluster or Area sampling
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Convert a normal random variable to a standard normal variable and vice versa.
Compute probabilities and percentiles using the standard normal table.
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Determining the Mean, Variance, and Standard Deviation of a Discrete Random Variable
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Illustrate the nature of bivariate data;
Construct a scatter plot;
Describe shapes (form), trend (direction), and variation (strength) based on the scatter plot; and
Estimate strength of association between the variables based on a scatter plot.
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1. Illustrate:
Null hypothesis
Alternative hypothesis
Level of significance
Rejection region; and
Types of error in hypothesis testing
2. Calculate the probabilities of commanding a Type I and Type II error.
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1. Calculate the Pearson Product Moment Correlation Coefficient
2. Solve problems involving correlation analysis.
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Identify the independent and dependent variable;
Draw the best fit line on a scatter plot;
Calculate the slope and the y-intercept of the regression line;
Interpret the calculated slope and the y-intercept of the regression line;
Predict the value of the dependent variable given the value of the independent variable; and
Solve problems involving regression analysis.
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as βdistorted thinkingβ.
Operation βBlue Starβ is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Model Attribute Check Company Auto PropertyCeline George
Β
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
Β
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
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Andreas Schleicher presents at the OECD webinar βDigital devices in schools: detrimental distraction or secret to success?β on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus βManaging screen time: How to protect and equip students against distractionβ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective βStudents, digital devices and successβ can be found here - https://oe.cd/il/5yV
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
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This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
How to Split Bills in the Odoo 17 POS ModuleCeline George
Β
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
2. Learning Competencies
The learner will be able to:
1. Illustrate point and interval estimations;
2. Distinguish between point and interval estimation;
3. Identify point estimator for the population mean;
4. Compute for the point estimate for the population
mean;
5. Identify the appropriate form of the confidence
interval estimator for the population mean when
the population variance is known; and
6. Compute for the confidence interval estimate based
on the appropriate form of the estimator for the
population mean.
3. Point estimation is the process of finding a single
value, called point estimate, from a random
sample of a population, to approximate a
population parameter. The sample mean x is
the point estimate of the population mean ο,
and s 2 is the point estimate of population
variance ο³2
4. Example 1
The sample mean π₯ is 45.12 and the population
mean ο is 46.51. Here, the point estimate is
the single value 45.12.
A good point estimate is one that is unbiased. If
random sampling was done in the collection
of a set of data, and a sample mean is
computed out of these data to approximate
the population mean ο, then the point
estimate π₯ is a good point estimate.
5. Example 2
A teacher wanted to determine the average
height of Grade 9 students in their school.
What he did was to go to the one of the eight
sections in Grade 9 and then took their
heights. He computed for the mean height of
the students and got 165 cm.
6. Here, 165 cm is not a good point estimate of the
population mean. The teacher should have
randomly selected the members of his sample
from the entire population using either a
simple random sampling or systematic
random sampling.
7. A researcher should not expect the point
estimate to be exactly equal to the population
parameter. However, any point estimate used
should be as close as possible to the true
parameter.
Data should be carefully collected.
Sampling should be done at random, and the
sample size should be large especially when
the population distribution is not normal.
Different samples of size n taken from the
same population produce different results.
8. In the case of a sample mean π₯, the result is
affected by the presence of outliers. These are
data that are numerically too far from the rest
of the data.
9. Example 3
Consider the population consisting of values
(6,2,8,9,3). Find the population mean.
Observation x
1 6
2 2
3 8
4 9
5 3
οx=28
Now consider some possible samples of size 2
drawn without replacement from the population.
10. Sample Mean π Computation of π
(6,2) 4 (6+2)/2=4
(6,8) 7 (6+8)/2=7
(6,9) 7.5 (6+9)/2=7.5
(6,3) 4.5 (6+3)/2=4.5
Each mean x of each sample is a point estimate of
the population ο
11. Sample Mean π Computation of π
(6,2,8) 5.3 (6+2+8)/3=5.3
(6,2,9) 5.7 (6+2+9)/3=5.7
(6,2,3) 3.7 (6+2+3)/3=3.7
(2,8,9) 6.3 (2+8+9)/3=6.3
Each mean x of each sample is a point estimate of
the population ο. Each is typically different from
the population mean (ο=5.6)
Consider some samples of size 3 drawn from the same
population without replacement.
12. Sample Mean π Computation of π
(6,2,8,9) 6.25 (6+2+8+9)/4=6.25
(6,2,8,3) 4.75 (6+2+8+3)/4=4.75
(6,8,9,3) 6.50 (6+8+9+3)/4=6.50
(2,8,9,3) 5.50 (2+8+9+3)/4=5.50
Each mean x of each sample is a point estimate of
the population ο. Each is typically different from
the population mean (ο=5.6)
Consider some samples of size 4 drawn from the same
population without replacement.
13. Example 4
The following are the systolic blood pressures of
all teachers in a private high school. Compute
the population mean.
120 110 120 130 120
130 112 125 120 130
120 120 130 110 120
140 115 125 130 115
145 120 123 140 130
110 140 140 120 120
160 120 135 130 125
130 130 140 120 110
125 150 125 110 125
115 120 130 120 130
14. Example 5
Assume that the following systolic blood
pressures were randomly selected from the 50
observations in Example 4. Compute the
sample mean.
120 112 120 130 120
140 115 130 110 130
145 140 123 140 115
110 150 140 120 130
130 120 130 120 130
15. The sample mean π₯ =126.8 is still different
from the population mean ο=125.6
Perhaps, it is better to approximate the
population parameter by determining a range
of values within which the population mean is
most likely to be located instead of using the
point estimate.
The range of values is called confidence
interval.
16. In approximating the population mean by
determining a range of values within which it
is most likely to be located, confidence levels
are used. The confidence levels of 90%, 95%,
and 99% are usually chosen.
Confidence interval uses interval estimate to
define a range of values that includes the
parameter being estimated with a specified
level of confidence.
17. Confidence level refers to the probability that
the confidence interval contains the true
population parameter. Its value is
confidence level=(1-ο‘)100%,
where ο‘=probability that the confidence
interval does not contain the true population
parameter.
18. The value of alpha ο‘ corresponds to the level
of significance. The value of alpha ο‘ can be
arbitrarily chosen. Any number between 0 and
1 can be used for alpha ο‘ but 0.10, 0.05, and
0.01 are the ones that are commonly used.
A 95% confidence level implies that the
probability of the confidence interval
containing the true population parameter is
95%.
19. Critical value is the value that indicates the
point beyond which lies the rejection region.
This region does not contain the true
population parameter.
21. Formula for interval estimate of population
mean when population variance is known and
n> 30.
where
22. For a specific value, ο‘=0.05, the distribution of xβs
is:
The mean of a random sample of size n is usually
different from the population mean ο. The
difference which is added to and subtracted from
the sample mean in the computation of
confidence interval is considered an error. In the
formula for confidence interval it is equal to
23. The confidence interval can be written as
where
To find the margin of error, use the following formula:
If n<30, the original population should be normally distributed
and the sample is drawn at random. The values at each end of
the interval are called confidence limits. The value at the left
endpoint of the interval is the lower confidence limit and the
value at the right endpoint of the interval is the upper
confidence limit. Between these limits lies the true population
parameter.
24. Example 6
The mean score of a random sample of 49 Grade
11 students who took the first periodic test is
calculated to be 78. The population variance is
known to be 0.16.
a. Find the 95% confidence interval for the
mean of the entire Grade 11 students.
b. Find the lower and upper confidence limits.
25. Solution
Step1. Find the π§πΌ
2
. Given π₯ = 78, π2
= 0.16, π = 49
Confidence level is 95%.
1 β πΌ 100% = 95%
1 β πΌ 1 = 0.95
1 β πΌ = 0.95
πΌ = 0.05
πΌ
2
= 0.025
Subtract 0.5 β 0.025 = 0.475 or 0.4750
Locate the area 0.4750 to z-table to determine the
corresponding z-value.
26.
27. Hence, π§πΌ
2
= 1.96
Step2. Find π, then find the margin of error E.
π = π2
= 0.16
= 0.4
Solve for E
πΈ = π§πΌ
2
π
π
= 1.96
0.4
49
= 0.112
28. Step3. Substitute the values of π₯ and E in the coefficient
interval π₯ β πΈ < π < π₯ + πΈ.
π₯ β πΈ < π < π₯ + πΈ
78 β 0.112 < π < 78 + 0.112
77.888 < π < 78.112
77.89 < π < 78.11
29. Conclusion:
The researcher is 95% confident that the sample
mean 78 differs from the population mean by
no more than 0.112 or 0.11. Also, the
researcher is 95% confident that the
population mean is between 77.89 and 78.11
when the mean of the sample is 78.
30.
31.
32. Example 7
Assuming normality, use the given confidence level
and sample data below to find the following:
a. Margin of error
b. Confidence interval for estimating the
population parameter
Given data:
99% confidence level
n=50
x=18,000
ο³=2,500
34. Step2. Find the margin of error.
πΈ = π§πΌ
2
π
π
= 2.575
2,500
50
= 910.40
35.
36.
37. Conclusion:
The researcher is 99% confident that the sample
mean 18,000 differs from the population
mean by no more than 910.40. The value of
the population mean is within the interval
17,089.60 and 18,910.40.
40. The point estimate for the difference of two
populations means To obtain
this point estimate, select two independent
random samples, one from each population
with sizes n1 and n2, then, compute the
difference between their means.
41.
42.
43. Example 8
Two groups of students in Grade 9 were subjected to two
different teaching techniques. After a month, they
were given exactly the same test. A random sample of
60 students were selected in the first group and
another random of 50 students were selected in the
second group. The sampled students in the first group
made an average of 84 with the standard deviation of
8, while the sampled students in the second group
made an average of 78, with a standard deviation of 6.
Find a 95% confidence interval for the difference in the
population means. The mean score of all students in
the first group is ο1 and the mean score of all students
in the second group is ο2
45. Step2. Find the value of π§πΌ
2
. Confidence level is 95%.
1 β πΌ 100% = 95%
1 β πΌ = 0.95
πΌ = 0.05
πΌ
2
=
0.05
2
= 0.025
0.500 β 0.025 = 0.475
Using the areas under the normal curve table, π§πΌ
2
=
1.96
46.
47. Example 9
Independent random samples were selected
from two populations. The sample means,
known population variance, and sample sizes
are given in the following table:
Find a 90% confidence interval for estimating
the difference in the population means
π1 β π2 .
Population 1 Population 2
Sample mean 34 38
Population variance 5 7
Sample size 40 46
48. Solution
Step1. Write the given information
Step2. Find the value of π§πΌ
2
. Confidence level is 90%.
Population 1 Population 2
π₯1 = 34 π₯2 = 38
π1
2 = 5 π2
2 = 7
π1 = 40 π2 = 46
1 β πΌ 100% = 90%
1 β πΌ = 0.90
πΌ = 0.1
πΌ
2
=
0.1
2
= 0.05
0.500 β 0.05 = 0.45
The area to the right of π§πΌ
2
is
0.05.
The area to the left of π§πΌ
2
is 0.05.
From the areas under the
normal curve table, π§πΌ
2
= 1.645
50. Step4. Find the confidence interval
π₯1 β π₯2 β πΈ < ππ β ππ < π₯1 β π₯2 + πΈ
34 β 38 β 0.87 < ππ β ππ < 34 β 38 + 0.87
β4 β 0.87 < ππ β ππ < β4 + 0.87
β4.87 < ππ β ππ < β3.13
It is possible that the difference between the two
population means π1 β π2 could be negative. This
indicates that the mean of population 1 could be
less than that of population 2.
52. The size of the sample is important in estimating the
population mean π. The following formula can be used to
determine the appropriate sample size.
Sample size for Estimating π:
π =
ππΆ
π
π
π¬
π
where π§πΌ
2
=
ππππ‘ππππ π£πππ’π πππ ππ ππ π‘βπ πππ ππππ ππππππππππ πππ£ππ
πΈ = πππ ππππ ππππππ ππ πππππ
π = ππππ’πππ‘πππ π π‘ππππππ πππ£πππ‘πππ
53. Example 10
Find the minimum sample size required to
estimate an unknown population mean π using
the following given data.
a. Confidence level = 95%
Margin of error = 75
π = 250
b. Confidence level = 90%
Margin of error = 0.891
π2
= 9
57. Step2. π = π2
= 9
= 3
π =
π§πΌ
2
π
πΈ
2
=
1.645(3)
0.891
2
= 30.68 ππ 31
The minimum sample size
required to estimate an
unknown population mean π
using the given data above is
31.
58. Example 11
A researcher wants to estimate the daily
expenses of college students. He wants a 99%
confidence level and a 40 margin of error. How
many students must he randomly select if in the
previous survey, π = 99.50?