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Confidence Intervals: Z -Interval for Means

Confidence Intervals: Z -Interval for Means. 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.

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Confidence Intervals: Z -Interval for Means

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  1. Confidence Intervals:Z-Interval for Means

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

  4. 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. Another error is to incorrectly state the meaning of a confidence interval. Following these steps will help you to avoid those problems.

  5. Step 1: Step 2: 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. Z-interval for means Assumptions: • We are given an SRS. • The population is stated to be normal. • σ is known.

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

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

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