Confidence Intervals for a Population Mean, Standard Deviation Unknown.

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Presentation transcript:

Confidence Intervals for a Population Mean, Standard Deviation Unknown

Student’s t-Distribution

Assumptions 1.sample data come from a simple random sample or randomized experiment 2.sample size is small relative to the population size (n < 0.05N) 3.the data comes from a population that is normally distributed, or the sample size is large

1.Find the area in one tail 2.Find Degree of Freedom: DF = n – 1 3.Look up the value in t-distribution table

1. Find the t-value such that the area in the right tail is 0.10 with 12 degrees of freedom

2. Find the t-value such that the area in the right tail is 0.05 with 20 degrees of freedom

3. Find the t-value such that the area left of the t-value is 0.01 with 9 degrees of freedom

4. Find the t-value that corresponds to 90% confidence. Assume 15 degrees of freedom

Confidence Interval

TI-83/84 Instructions

5. Determine the point estimate of the population mean and margin of error for each confidence interval Lower bound: 20, upper bound: 28

6. Confidence Interval (By Hand and By TI-83/84) A simple random sample of size 25 has a sample mean of 20.2 and a sample standard deviation of 2.1, construct a 95% confidence interval for the population mean (assume data is normally distributed)

7. Confidence Interval (By Hand and By TI-83/84) Ages of students at the college follow a normal distribution. If a sample of 15 students has an average age of 18.2 with a standard deviation of 0.5. Construct a 99% confidence interval for the population mean

8. Confidence Interval (By Hand and By TI-83/84) A sample of scores are listed below (assume the scores are normally distributed), construct a 90% interval for the population mean: