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AP Stats 7.3 Quiz
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A manufacture claims that only 2% of their products are defective. A store takes delivery of 300 items from the manufacture. Let X = the number of defective items. Assuming the manufacture is correct that only 2% of their products are defective, what are the mean and standard deviation of the sampling distribution of X?
The mean number of defective items is 6 and the standard deviation is 5.88.
The mean number of defective items is 6 and the standard deviation is 2.42.
The mean number of defective items is 2 and the standard deviation is 5.88.
The mean number of defective items is 2 and the standard deviation is 2.42
Ninety percent of the students at a high school are right-handed. Which of the following sample sizes is the smallest that satisfies the large count condition to approximate the distribution as a normal distribution?
A random sample of 120 students at a certain high school was asked if they spend more than 4 hours a night on homework. Assume the true proportion of students that spend more than 4 hours a night on homework is 15%, which of the following is closest to the probability that more than 20% of the students in a sample would respond that they spend more than 4 hours a night on homework?
The distribution of the number of siblings students at a local high school have has a mean of 2.2 siblings and a standard deviation of 1.4 siblings. Suppose we select a random sample of 40 students at the high school.
Let "x-bar" = the sample mean number of siblings for students in your sample. What is the standard deviation of the sampling distribution of "x-bar"and what does it mean?
In SRSs of size 40 from the high school, the sample mean number of siblings in the sample would typically vary by about 6.32 from the true average of 2.2 siblings.
In SRSs of size 40 from the high school, the sample mean number of siblings in the sample would typically vary by about 1.4 from the true average of 2.2 siblings.
In SRSs of size 40 from the high school, the sample mean number of siblings in the sample would typically vary by about 0.22 from the true average of 2.2 siblings.
In SRSs of size 40 from the high school, the sample mean number of siblings in the sample would typically vary by about 0.035 from the true average of 2.2 siblings.
A sample of size n = 100 was taken from the residents in a large city to estimate the average number pets the residences own. The sample mean, "x-bar" , was 1.91 pets. Suppose m, the true mean number of pets owned by residents in the city, is 1.75 pets with a standard deviation, s, of 1.1 pets. What is the mean and the standard deviation of the sampling distribution of "x-bar"?
The mean is 1.91 pets and the standard deviation is 1.1 pets.
The mean is 1.91 pets and the standard deviation is 0.11 pets.
The mean is 1.75 pets and the standard deviation is 0.11 pets.
The mean is 1.75 pets and the standard deviation is 0.011 pets.
A company produces tortillas that are supposed to have an average diameter of 6 inches. Each of the tortillas the machine produces is slightly different, but the distribution diameters is approximately normal with a mean of 6.05 inches and a standard deviation of 0.2 inches. A bag that contains 10 tortillas claims the diameter of the tortillas in the bag is 6 inches. Suppose the 10 tortillas in the bag represent a random selection of all tortillas produced by the machine. What is the approximate probability that the mean diameter of the 10 tortillas in the bag is less than the claim of 6 inches?
The heights of the players on high school basketball teams in a certain state are approximately normally distributed with a mean of 73 inches and a standard deviation of 3.75 inches. Consider the local high school team to be a random selection of 11 players from the state. What is the approximate probability the 11 players on a team will have a mean height of less than 72 inches?
A sample of size n will to be taken from the residences in a large city to estimate the mean price of their home. The distribution of home values in the city is strongly skewed right. Which of the following is the smallest sample size such that the sampling distribution of is approximately normal?
Since the population is strongly skewed right, no sample size will have a sampling distribution that is approximately normal.
A sample of size 10 is the smallest sample size that will have a sampling distribution that is approximately normal.
A sample of size 30 is the smallest sample size that will have a sampling distribution that is approximately normal.
The central limit theorem guarantees that all samples of size n will have a sampling distribution that is approximately normal.
Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT Math scores. Suppose that you do this many, many times. Which of the following are the mean and standard deviation of the sampling distribution of
Mean = 515, SD = 114 100 \frac{114}{\sqrt{100}} 1 0 0 1 1 4
Mean = 515, SD = 114
Mean = 515/100, SD = 114/100
Mean = 515/100, SD = 114 100 \frac{114}{\sqrt{100}} 1 0 0 1 1 4
The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that
as we look at more and more bulbs, their average burnout time gets ever closer to the mean μ for all bulbs of this type.
the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.
the average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal.
the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.
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Monday, february 3, 2020, 7.3 sampling distribution of mean, no comments:, post a comment, summary of material for from this year.
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Helping math teachers bring statistics to life
What is a Sampling Distribution? Day 1
Chapter 7 - day 1 - lesson 7.1, all chapters, learning targets.
Distinguish between a parameter and a statistic.
Create a sampling distribution using all possible samples from a small population.
Distinguish among the distribution of a population, the distribution of a sample, and the sampling distribution of a statistic.
Activity: What was the average for the Chapter 6 Test?
Answer Key:
In this Activity, students will be trying to estimate the mean test score for a population using a the mean calculated from a sample. We start with a very simple and unrealistic population of 4 students. We do this to help students build the idea that a sampling distribution contains allof the possible samples from the population (easy to do with such a small population). Tomorrow we will be more realistic and look at the actual population of all AP Stats students.
Where are we headed?
Noti ce the organization of this Chapter.
Section 7.1 is an introduction to sampling distributions, which includes sampling distributions for proportions and sampling distributions for means. Actually it includes sampling distributions for any statistic.
Section 7.2, we investigate the shape, center, and variability of the sampling distribution of a sample proportion.
Section 7.3, we investigate the shape, center, and variability of the sampling distribution of a sample mean.
The Activity uses a sampling distribution for a sample mean. The Check Your Understanding problem uses a sampling distribution for a sample proportion.
Have I seen this before?
This is not our students first experience with sampling distributions. We have intentionally given them previous experiences in preparation for today’s lesson. In Chapter 4, we took samples of 5 words from from Beyonce’s Crazy in Love in order to estimate the mean word length. We also took samples of Justin Timberlake fans to find the mean enjoyment level. Hopefully you made dotplot posters for these activities and you can refer back to them in this Chapter.
Notation matters.
Starting right now, we are going to be crazy about using the correct notation. Notation is wonderful because we can show several ideas at once (is this value from a sample or a population?, is this value a mean or a proportion?).
Population distribution, distribution of a sample, or a sampling distribution?
All three of these distributions can be represented with a dotplot in the Activity. In a population distribution (#1), each dot represents one individual from the population (and we have a dot for every individual). In a distribution of a sample, each dot represents one individual from the population (but we don’t have every individual…only a sample of 2). In a sampling distribution (#4), each dot represents a sample from the population and a mean calculated from that sample.The common error that students make is to use the term “sample distribution” when they mean “sampling distribution”. A sample distribution is the distribution of values for one sample. A sampling distribution represents many, many samples.
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Hypothesis Testing pdf : Section 9.1 Section 9.2 Section 9.3 Day 1 Section 9.3 Day 2 Section 9.1 & 9.2 Error and Power
Inference for 2 proportions: 2 Proportions – CI & Sig Test
Inference for 2 means: 2 Means – CI & Sig Test
Chi-squared testing: Chi-squared – Goodness of fit , Chi-squared – Independence ,
Inference for Regression: Inference for Regression
PDF files :
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Inference for 2 means: 2 Means
Chi-squared testing: Chi-squared – Goodness of fit , Chi-squared – Independence
Inference for Regression: Inference for Regression
Chapter 6, Sections 1 & 2 , Chapter 6, Section 3
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7.1 the central limit theorem for sample means (averages).
In a population whose distribution may be known or unknown, if the size ( n ) of the sample is sufficiently large, the distribution of the sample means will be approximately normal. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, called the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size ( n ).
7.2 The Central Limit Theorem for Sums (Optional)
The central limit theorem tells us that for a population with any distribution, the distribution of the sums for the sample means approaches a normal distribution as the sample size increases. In other words, if the sample size is large enough, the distribution of the sums can be approximated by a normal distribution, even if the original population is not normally distributed. Additionally, if the original population has a mean of μ X and a standard deviation of σ x , the mean of the sums is nμ x and the standard deviation is ( n ) ( n ) ( σ x ), where n is the sample size.
7.3 Using the Central Limit Theorem
The central limit theorem can be used to illustrate the law of large numbers. The law of large numbers states that the larger the sample size you take from a population, the closer the sample mean, x ¯ x ¯ , gets to μ .
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IMAGES
VIDEO
COMMENTS
Take all samples. data is normal. Proportions. np & n (1-p) are 10+. Means. normal distribution or sample of 30+. SD always done. if I works. Study with Quizlet and memorize flashcards containing terms like Mean of Sampling Distribution, SD of Sampling Distribution, Regardless of original population shape and more.
step 3: check large counts condition; np>=10 and n (1-p)>=10. step 4: if all above works, use normal approximation & five step summary. five step summary for proportions. 1) p (x>0.33) 2) p (z> 0.33- proportion or % given/ SD) = p (z> ) 4) normal cdf (lower=0.33, upper= 9999, u=0, o=1) 5) The probability that the random sample of 1500 students ...
AP Statistics Link to Chapter 7 Video Notes. YOUTUBE PLAYLIST CHAPTER 7. Power Points & Notes Outline ... AP Notes Chapter 7 Homework. Key HW 7.1 Part A problems 1-8 ... Examples for 7-3 are below. Mean and Standard Deviation of X-bar. Probability involving sample mean.
Stats 7.3. Mean and Standard Deviation of the Sampling Distribution of x̅. Click the card to flip 👆. Suppose that x̅ is the mean of an SRS of size n drawn from a large population with mean µ and standard deviation σ, then: The mean of the sampling distribution of x̅ is µ of x̅ = µ. The standard deviation of the sampling distribution ...
AP Stats 7.3 Quiz quiz for 12th grade students. Find other quizzes for Mathematics and more on Quizizz for free! ... A random sample of 120 students at a certain high school was asked if they spend more than 4 hours a night on homework. Assume the true proportion of students that spend more than 4 hours a night on homework is 15%, which of the ...
AP Statistics Monday, February 3, 2020. 7.3 Sampling Distribution of Mean 7.3 day 1 notes 7.3 day 2 notes - CLT Homework due 2/11 p. 462-464 #50-64even, 65-72, FRAPPY 7.1-7.2 Quiz on Thursday Straub - Chapter 7 test on 2/13 Quiz on 7.3 and 8.1 Friday 2/14 at February 03, 2020.
How to Write a Great Test for AP Statistics. How to Grade Your AP Statistics Tests. AP Free Response Questions that you can use on the Chapter 7 Test. Questions to be Sure to Include. Make sure that one of the questions requires students to do inferential thinking. This will require them to first do a probability calculation and then to answer ...
7.2 - Sample Proportions. Choose an SRS of size n from a large population with population proportion p having some characteristic of interest. Let be the proportion of the sample having that characteristic. Then the mean and standard deviation of the sampling distribution of are. Mean:
Sample proportions arise most often when we are interested in categorical variables. 2. Sample means are used use quantitative variables we are interested in other statistics such as the median or mean or standard deviation of the variable. Example: Consider the mean household earnings for samples of size 100.
Notice the organization of this Chapter. Section 7.1 is an introduction to sampling distributions, which includes sampling distributions for proportions and sampling distributions for means. Actually it includes sampling distributions for any statistic. Section 7.2, we investigate the shape, center, and variability of the sampling distribution ...
View step-by-step homework solutions for your homework. Ask our subject experts for help answering any of your homework questions! ... PRACTICE OF STATISTICS F/AP EXAM 6th Edition, Starnes. BUY THIS BOOK BUY. PRACTICE OF STATISTICS F/AP EXAM. 6th Edition. Starnes. Publisher: MAC HIGHER. ISBN: 9781319113339.
7.3 - sample means. divider. where sample mean is centered. when we choose many SRS's from a population, the sampling distribution of the sample mean is centered at the population mean "µ" and is less spread out than the population distribution. mean and std. dev of the sampling distribution of x̄.
3 min read. 7.8. Setting Up a Test for the Difference of Two Population Means. 4 min read. 7.9. Carrying Out a Test for the Difference of Two Population Means. 3 min read. 7.10. Skills Focus: Selecting, Implementing, and Communicating Inference Procedures.
AP Statistics PowerPoints. Unit 1: Chapter 1 Notes Edition 5. Chapter 2 Notes Edition 5. Unit 2: Chapter 3 PowerPoint 2013-2014, ...
AP 7.3 Guided Notes for Reading Textbook (KEY) AP Stats Chapter 7 - Glossary of Important Definitions. Notes (PowerPoint Presentation) AP Stats 7.1 Sampling Distribution. AP Stats 7.2 Sampling Proportions. AP Stats 7.3 Sampling Means. In-Class Activities.
Book Details. The most thorough and exciting revision to date, The Practice of Statistics 4e is a text that fits all AP Statistics classrooms. Authors Starnes, Yates and Moore drew upon the guidance of some of the most notable names in AP and their students to create a text that fits today's classroom. The new edition comes complete with new ...
Ch 1.1 Practice. Ch 1 Test (Quantitative Data) Ch 1.2 Check Your Understanding. Ch 1.2 / 1.3 Graphing Calculator Practice. Battery Intro. Ch 3 Test (Scatterplots and Least-Squares Regressions) Linear Regressions and Scatterplots. Forensic Lab. Practice with Residuals.
AP Statistics Chapter 7 Multiple Choice Questions. 6 terms. Jordyn_Vu. Preview. Unit 6 Progress Check: MCQ Part A (AP STATS) 12 terms. kate4994. Preview. AP Statistics Chapter 8 Formulas. Teacher 13 terms. Colleen_Rossetti. Preview. Stats 1430 Final Exam. 53 terms. Peyton58122. Preview. Statistics. 30 terms. saraharb1. Preview. Unit 3 Stats .
Introduction; 9.1 Null and Alternative Hypotheses; 9.2 Outcomes and the Type I and Type II Errors; 9.3 Distribution Needed for Hypothesis Testing; 9.4 Rare Events, the Sample, and the Decision and Conclusion; 9.5 Additional Information and Full Hypothesis Test Examples; 9.6 Hypothesis Testing of a Single Mean and Single Proportion; Key Terms; Chapter Review; Formula Review
Sampling Methods}AP Free Response: H: 4.2: Experimental Design}AP Free Response: W : Lurking Variables: H: 4.3: Planning and Conducting A Study (College Board) H: Chapter 4: Homework Solutions: H : Notes: H : Review Problems (Request through e-mail) W : 5.1: Random Digit Table: H : Simulations}AP Fee Response, The Monty Hall Problem: W : The ...
the distribution of values taken by the statistic in all possible samples of the same size from the same population. In statistics this term is used for any finite or infinite collection of 'units', which are often people but may be, for example, institutions, events, etc. The distribution of values of the variable for the individuals included ...
3.2 Teacher Items. Handout Key: pdf, docx. Slide Deck: ppt, pdf. CED/Textbook Alignment: page. Data: xlsx. All Part 3 Lessons. AP Statistics lesson 3.2, from the Skew The Script curriculum. Covers educational inequity (income achievement gap) through linear regression on attendance.