Chapter 8 - Parameter Estimation

Question 1

What is a critical value of a statistic?

Answer 1

The value of a statistic that marks the boundary of a specified area (such as .05 or 0.1) in the tail of a distribution.

Question 2

What is a point estimate?

Answer 2

A computed statistic that approximates a parameter.

A single value given as an estimate of a parameter of a population.

Question 3

What is an unbiased estimator?

Answer 3

A point-estimate such that if we repeated the point-estimating process infinitely often, the same number of point-estimates would be too high as too low.

Question 4

What is a 95% confidence interval?

Answer 4

A range of values that has a 95% probability of containing the actual value of a parameter.

Question 5

What is the level of confidence?

Answer 5

The probability that a given confidence interval contains the actual value of the parameter.

Question 6

Where is the confidence level centered on?

Answer 6

The confidence level is centred on x (mean of sample) and extends about two standard errors in each direction. Note the x needs a - above it.

Question 7

Steps for eyeball estimating a confidence interval when the standard deviation of a population is known.

Answer 7

1. Eyeball-estimate the sample mean
2. Ascertain population standard deviation
3. Divide the known standard deviation by square root of sample size to obtain the standard deviation of the mean of the sample.
4. Double the standard deviation of the sample mean.
5. Both subtract and add that result to the mean of the sample.

Question 8

Finish this sentence - The more confidence you require…

Answer 8

the wider the confidence interval must be.

Question 9

What are student’s t distributions?

Answer 9

A family of distributions that, like z (standard score), are unimodal, symmetric, and asymptotic, but the exact shape (unlike z) depends on the degrees of freedom.

Question 10

Who is William S Gossett?

Answer 10

The observation that the confidence interval must be wider when the standard deviation of a population is unknown was first made in the early 1900s by William S Gossett, a chemist at an Irish brewery. He wrote under the pen name ‘student’.

Question 11

Box 8.5

Answer 11

see p. 192

Question 12

What are the four factors that affect the width of a confidence interval?

Answer 12

1. Increasing the sample size makes the confidence interval narrower.
2. Decreasing standard deviation of a population or the standard deviation of a sample makes the confidence interval narrower.
3. The confidence interval when standard deviation of a population is known is generally narrower than when the standard deviation of a population is unknown.
4. Decreasing the level of confidence makes the confidence interval narrower.