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Confidence Intervals: Z-Interval for Means

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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, and there will be more in the future. 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. σ X : 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.

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

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It is a significant amount of writing to include these steps in finding a confidence interval. The reason for doing this is in steps is to give you a frame- work that works for these intervals and for those to come. A common student error is to fail to show how assumptions are met. Listing the assumptions is not enough. Following these steps will help you to avoid those problems. Another error is to incorrectly state the meaning of a confidence interval.

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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.

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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.

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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:

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