Download presentation

Presentation is loading. Please wait.

Published byTyrese Kurk Modified over 3 years ago

1
Confidence Intervals

2
Whenever we make a confidence interval we should follow these steps to be sure that we include all parts: State the type of interval (our first intervals are Z-intervals) Meet assumptions (explain how each is met) SRS: Our sample must be a random selection of the population. Normality: The sampling distribution must be approximately normal. : The population standard deviation must be known. Write the formula. Substitute values into the formula and give the result. Communicate the meaning of the confidence interval in terms of the original problem.

3
So, by topic: Step 1: Type of interval Step 2: Assumptions Step 3: Formula and calculations Step 4: Conclusion

4
It is a significant amount of writing to include these steps in finding a confidence interval. The reason for doing this is to give you a framework to follow so that each problem follows a set format. It will be easier in the long run to be used to following a set format. A major complaint by those who grade AP Statistics exams is that AP students sometimes fail to meet assumptions or explain what a confidence interval means. Following these steps will help you to avoid those problems.

5
Problem: For the year 2000, SAT Math scores had a mean of 514 and a standard deviation of 113. SAT Math scores follow a normal distribution. A random sample of students at Horsehead High had the following SAT Math scores: {550, 480, 510, 460, 600, 570}. Find a 95% confidence interval for the SAT Math scores at Horsehead High. Step 1: Z-interval for means Step 2: Assumptions: We are given an SRS. The population is stated to be normal. σ is known.

6
Step 3: or Step 4: We are 95% confident that the true mean SAT math score at Horsehead High lies between 437.9 and 618.8.

7
If we select many random samples of 6 and compute confidence intervals this way, 95% of the time we will capture the true mean. If asked what 95 % confidence means,

8
Assumptions for Z Confidence Intervals and Tests of Significance

9
Whenever we make a confidence interval or test of significance we must be certain that we meet theoretical assumptions before we may make the actual interval or test. Our tests and intervals cannot be applied to all circumstances. Fortunately, they do work in many circumstances, and we will be able to verify that this is so. The assumptions are the same for confidence intervals and tests of significance, so we have only one set to learn.

10
If we can tell from the problem statement or context that an assumption is not met, we must state so, and our results will be suspect. What if we don ’ t meet the assumptions? Due to the educational nature of this class, I will ask you to go ahead and work the problem, anyway, even if the assumptions are not met (but you must state that they are not met). In the real world, we would have to meet the assumption before proceeding, but because we are unable to redo an experiment, for example, we will use the information we have.

11
The first assumption is that our sample is a simple random sample, usually abbreviated SRS. This information is usually provided in the problem. If so, we can simply state that SRS is given. Sometimes we will have no information about how the sample was made, and in that circumstance we can write that we are uncertain that we have an SRS. 1 st Assumption:

12
The simple random sample is so important because it avoids bias that may be the result of selection. Our sample should be representative of the population, otherwise we may draw conclusions about a group different from the one we wanted. Recall that randomization was an important principle of experimental design, and this is why! Randomization guarantees random samples. If we can tell that our sample is not an SRS, we must state that. It may mean that our results are not valid.

13
The second assumption is that our sampling distribution is normally distributed. This assumption is met whenever our population is normally distributed. This information may be provided in the problem, and if so, we simply write that it is given that the population is normal. A principle that often helps us here, is the Central Limit Theorem. As sample size becomes large the sampling distribution approaches the normal distribution, even if the original population is not normal. When we have large samples, we invoke the CLT. 2 nd Assumption:

14
Otherwise, we must examine the data provided in an effort to see whether or not it is reasonable to expect the sampling distribution to be normal. We will spend more time on exactly what to do here later in the course.

15
Our third and final assumption is that σ is known. This must be provided to you in the problem, otherwise we cannot use the Z-interval or test. In Module 11, we will learn what to do when σ is unknown. 3 rd Assumption:

16
In summary: SRS Whenever we perform statistical inference using a Z test or interval for sample means, we need: Normal distribution of sampling distribution σ (the population standard deviation)

Similar presentations

OK

From Theory to Practice: Inference about a Population Mean, Two Sample T Tests, Inference about a Population Proportion Chapters 17-18-etc.

From Theory to Practice: Inference about a Population Mean, Two Sample T Tests, Inference about a Population Proportion Chapters 17-18-etc.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on campus recruitment system analysis One act play ppt on website Ppt on law against child marriage Ppt on mars one astronaut Ppt on lcd tv technology Ppt on us polo brand Ppt online mobile shopping Ppt on nutrition in animals class 7 Ppt on travel and tourism industry Ppt on human resource department