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2 How perform I construct and analyze Confidence Intervals using the margin of error?

3 Rate your confidence Shooting a basketround at a wading pool, will make basket? Shooting the ball at a big trash have the right to, will make basket? Shooting the ball at a carnival, will certainly make basket?

4 What happens to your confidence as the interval gets smaller?The larger your confidence, the broader the interval.

5 Confidence Interval An interval that is computed from sample data and also provides a selection of plausible worths for a population parameter Is the success price of the method supplied to construct the interval Formula: Typical of the sample + margin of error

6 Construct: 65.25 ± 4.50 produces an interval from 60.75 to 69.75Interpret: We are 95% confident the interval from \$60.75 to \$69.75 contains the actual suppose amount of money teenagers spend on music per month.

7 Margin of error Shows exactly how precise we believe our estimate isThe smaller the margin of error, the more specific our estimate of the true parameter Formula:

8 Critical Values There are 4 typical levels of confidence: 99%, 98%, 95% and also 90%. Level of confidence Z – Critical Values 90% 1.645 95% 1.96 98% 2.33 99% 2.576

9 Confidence interval for a populace mean:Standard deviation of the statistic Critical value Estimate/suppose of sample Margin of error

10 Steps for doing a confidence interval:Assumptions – SRS from populace Sampling circulation is normal (or about normal) Given (normal) Large sample dimension (about normal) Graph information (around normal) s is recognized Calculate the interval Write a statement around the interval in the conmessage of the problem.

11 Statement (interpret): (memorize!!)We are ________% confident that the true suppose context lies within the interval ______ and ______.

12 A test for the level of potassium in the blood is not perfectly exact. Suppose that repeated measurements for the very same perkid on various days differ generally with s = A random sample of 3 has a suppose of What is a 90% confidence interval for the mean potassium level? Assumptions: Have an SRS of blood measurements Potassium level is usually spread (given) s known We are 90% confident that the true intend potassium level is between 3.01 and also 3.39.

13 Have an SRS of blood measurements 95% confidence interval? Assumptions: Have an SRS of blood measurements Potassium level is commonly spread (given) s well-known We are 95% confident that the true intend potassium level is between 2.97 and 3.43.

14 99% confidence interval? Assumptions: Have an SRS of blood measurements Potassium level is usually spread (given) s recognized We are 99% confident that the true intend potassium level is between 2.90 and 3.50.

15 the interval gets broader as the confidence level increasesWhat happens to the interval as the confidence level increases? the interval gets broader as the confidence level rises

16 A random sample of 50 CHHS students was taken and also their intend SAT score was (Assume s = 105) What is a 95% confidence interval for the suppose SAT scores of CHHS students? We are 95% confident that the true intend SAT score for CHS students is in between and

17 Suppose that we have this random sample of SAT scores: What is a 95% confidence interval for the true mean SAT score? (Assume s = 105) We are 95% confident that the true intend SAT score for CHHS students is in between and also

18 In a randomized comparative experiment on the results of calcium on blood pressure, researchers split 54 healthy and balanced males at random into 2 groups, takes calcium or placebo. The paper reports a suppose seated systolic blood pressure of via typical deviation of 9.3 for the placebo group. Assume systolic blood pressure is usually spread.

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19 For the Ex. 4: Find a 95% confidence interval for the true expect systolic blood press of the placebo group. Assumptions: Have an SRS of healthy and balanced males Systolic blood push is generally spread (given). s is unwell-known We are 95% confident that the true intend systolic blood push is between and

21 Why is the Central Limit Theorem important in statistics…

22 A sample of 300 high institution students was asked just how many text messperiods they sent on a given day. The suppose was 38 via a standard deviation of 17.5. (a) If we had 49 such samples, what would certainly we mean the intend and traditional deviation of the sampling circulation of means to be?

23 Ex. 5 – A clinical researcher measured the pulse rate of a random sample of 20 adults and uncovered a intend pulse rate of beats per minute via a standard deviation of 3.86 beats per minute. Assume pulse rate is usually spread. Compute a 95% confidence interval for the true intend pulse prices of adults. (70.883, )

24 Ex. – Consumer Reports tested 14 randomly schosen brands of vanilla yogurt and also discovered the adhering to numbers of calories per serving: Compute a 98% confidence interval for the average calorie content per serving of vanilla yogurt. (126.16, )

25 Find a sample size: 2

26 The heights of CHHS male students is generally dispersed through s = 2The heights of CHHS male students is typically dispersed through s = 2.5 inches. How large a sample is essential to be specific within inches with a 95% confidence interval? n = 43