Sampling Distribution Characteristics I
- The shape will be normal because the population is normal (or \(n\geq30\)).
- The center will be equal to 100 because \(\bar{x}\) is an unbiased estimator of \(\mu\)=100.
- This is the same as the SE which is \(\frac{\sigma}{\sqrt{n}}\)=\(\frac{20}{\sqrt{50}}\)=2.83.
- This is the same as the previous question, i.e., 2.83.
Sampling Distribution Characteristics II
- The shape will be normal because \(n\geq30\).
- The center will be equal to 500 because \(\bar{x}\) is an unbiased estimator of \(\mu\)=500.
- This is the same as the SE which is \(\frac{\sigma}{\sqrt{n}}\)=\(\frac{60}{\sqrt{100}}\)=6.
- This is the same as the previous question, i.e., 6.
Sampling Distribution Characteristics III
- The shape will be normal because \(n\geq15\) and the population is only slightly skewed.
- The center will be equal to 500 because \(\bar{x}\) is an unbiased estimator of \(\mu\)=500.
- This is the same as the SE which is \(\frac{\sigma}{\sqrt{n}}\)=\(\frac{60}{\sqrt{20}}\)=13.42.
- This is the same as the previous question, i.e., 13.42.
Accuracy and Precision
- The 9, 10, 11, and 9 means are more accurate.
- The 6, 14, 8, and 12 means are more accurate.
- The 7, 7, 9, and 8 means are more precise.
- The 2,8,12, and 18 means are accurate, but imprecise.
- The means 9,10,11, and 10 are accurate and precise.
- The means 1,7,8, and 19 are inaccurate and imprecise.