The population distribution is normally distributed and has a mean of 13.6 and a standard deviation of 3.0. These values are unknown to a researcher who samples individuals to estimate a mean. Suppose she takes a random sample of 23 individuals. What is the sampling distribution? Find the 95% confidence interval for the mean. Suppose that they found a sample with a mean number given by y¯ = 15. Is this unusual?

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The population distribution is normally distributed and has a mean of 13.6 and a standard deviation of 3.0. These values are unknown to a researcher who samples individuals to estimate a mean. Suppose she takes a random sample of 23 individuals.

  1. What is the sampling distribution?
  2. Find the 95% confidence interval for the mean.
  3. Suppose that they found a sample with a mean number given by y¯ = 15. Is this unusual?
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