Sampling Distribution Characteristics I

  1. The shape will be normal because the population is normal (or \(n\geq30\)).
  2. The center will be equal to 100 because \(\bar{x}\) is an unbiased estimator of \(\mu\)=100.
  3. This is the same as the SE which is \(\frac{\sigma}{\sqrt{n}}\)=\(\frac{20}{\sqrt{50}}\)=2.83.
  4. This is the same as the previous question, i.e., 2.83.

Sampling Distribution Characteristics II

  1. The shape will be normal because \(n\geq30\).
  2. The center will be equal to 500 because \(\bar{x}\) is an unbiased estimator of \(\mu\)=500.
  3. This is the same as the SE which is \(\frac{\sigma}{\sqrt{n}}\)=\(\frac{60}{\sqrt{100}}\)=6.
  4. This is the same as the previous question, i.e., 6.

Sampling Distribution Characteristics III

  1. The shape will be normal because \(n\geq15\) and the population is only slightly skewed.
  2. The center will be equal to 500 because \(\bar{x}\) is an unbiased estimator of \(\mu\)=500.
  3. This is the same as the SE which is \(\frac{\sigma}{\sqrt{n}}\)=\(\frac{60}{\sqrt{20}}\)=13.42.
  4. This is the same as the previous question, i.e., 13.42.

Accuracy and Precision

  1. The 9, 10, 11, and 9 means are more accurate.
  2. The 6, 14, 8, and 12 means are more accurate.
  3. The 7, 7, 9, and 8 means are more precise.
  4. The 2,8,12, and 18 means are accurate, but imprecise.
  5. The means 9,10,11, and 10 are accurate and precise.
  6. The means 1,7,8, and 19 are inaccurate and imprecise.