Lecture 6

Question 1

Point estimate

Answer 1

A point estimate is a single value estimate for a population parameter. For example an unbiased point estimate of the population mean, mu, is the sample mean, x flat roof.

Question 2

Interval estimation

Answer 2

Problem: point estimates are almost always “wrong”
Solution: calculate an interval that most likely contains the relevant parameter

Question 3

Level of confidence

Answer 3

The level of confidence is the probability that the population parameter is contained within the estimated interval

Question 4

Confidence interval

Answer 4

a type of interval estimates, 90%, 95%,99%

Question 5

Confidence interval - Ex conclusions

Answer 5

• When sampling from the same population using a fixed sample size, the higher the coverage rate, the wider the interval
• When sampling from the same population using fixed coverage rate, the larger the sample size the narrower the confidence interval
• However, it is a bad idea to make the confidence interval smaller by decreasing the coverage rate. If smaller interval is needed rather increase n.

Question 6

t-distribution, 6 properties

Answer 6

• The t-distribution is bell-shaped but with thicker tails than the standard normal distribution
• The t-distribution is symmetric around the man
• The t-distribution is a family of curves, each determined by a parameter called the degrees of freedom (df). The degrees of freedom are the number of free choices left after a sample statistic such as x roof is calculated. When you use a t-distribution to estimate a population mean, the degrees of freedom are equal to one less than the sample size
• df = n - 1
• The total are under a t-curve is 1 or 100%
• As the degrees of freedom increase, the t-distribution approaches the normal distribution. After around df = 30, the t-distribution is close to the standard normal distribution (Z)

Question 7

confidence intervals - t-distribution (notes)

Question 8

confidence intervals - nonnormal distribution (notes)