A study of college freshman study habits found that the time




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

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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?

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

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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

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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.

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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:

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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

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

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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.

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

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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.

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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.

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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.

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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

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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

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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

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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

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21 Why is the Central Limit Theorem important in statistics…

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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?

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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, )

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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, )

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25 Find a sample size: 2

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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

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