Estimation and Confidence Intervals

Question 1

Definition of statistical estimation

Answer 1

Estimate the parameter being investigated by finding the mean value from a random sample

Question 2

Definition of sample/point estimation

Answer 2

Use of sample data to calculate an estimate of an unknown parameter

Question 3

Definition of confidence interval

Answer 3

A range of plausible values for an unknown calue

Can quantify uncertainty and imprecision

Question 4

Definition of sampling error

Answer 4

Different samples give different estimates

Question 5

Definition of sample distribution

Answer 5

Sample estimates calculated from multiple ampler from the same population will have varying distribution values

Question 6

Definition of standard error

Answer 6

Indication of the extent of the sampling error
Tells us how much a sample mean tends to cary from the population mean
Provides and estimate of the precision of the sample mean

Question 7

How would you estimate a value from a large population

Answer 7

Impossible to measure everyone in a population

1. Take a random sample, find the sample mean
2. Different samples => different point estimates
3. Sample estimates vary around a true value
4. Can use this data to work out a confidence interval

Question 8

What is the confidence interval and what is it used for

What can it not tell you

Answer 8

Cannot deduce exact population value from a sample
Can use sample to obtain a confidence interval
-Range within which a population value is likely to be

Question 9

Describe the pathway in an investigation and show how you’d use the info found on the population parameter

Answer 9

Design a study based on the population parameter
Take a sample and estimate the parameter
Take the results and deduce that it applies to the whole population

Question 10

What is sampling error

How does it arise

Answer 10

Different samples => different estimates

Provide an incomplete picture of the population

Question 11

What 2 values help you find the true mean

Answer 11

Bigger sample size => estimate closer to true mean

Smaller SD => estimate closer to true mean

Question 12

What is the standard error

What is the equation for standard error

Answer 12

Tells you how much a sample mean tends to vary from the true population
Estimate of precision of sample mean

SE = SD/√N

Question 13

How do you increase precision if you can change the SD or the sample size

Answer 13

Decreased SD or increased sample size => smaller SE => increased precision

Question 14

What does it mean to have a 95% confidence interval

Answer 14

True mean expected to lie within range in 95% of calculations

Lower confidence limit = -1.96 SD of sample mean
Upper confidence limit = +1.96 SD of sample mean

Confidence interval = range between lower confidence limit and upper confidence limit

Question 15

What are the 3 assumptions in calculating the confidence interval

Answer 15

Normal data or large sample ≥60)
Sample chosen at random from population
Observations are independent of each other

Question 16

How do you calculate the lower confidence and upper confidence limit

How do you use these values to find the confidence interval for the mean

Answer 16

SE = SD/√N

Mean +- (1.96 x SE) = Upper and lower confidence limit

95% confident that the true mean lies between the LCL and UCL

Question 17

What are the 4 assumptions in estimating population proportions

Answer 17

Sample randomly chosen
Independent observations
Proportions with characteristic not close to 0 or 1
np and n(1-p) are >5 (large sample)

Question 18

How do you calculate SE for proportions

Answer 18

√(p(1-p))/n = SE

p = proportion with characteristic
(1-p) = proportion without characteristic

Question 19

How do you calculate the lower and upper confidence limit

How do you use these values to find the confidence intervals for a proportion of the population

Answer 19

p +-(1.96 x √p(1-p)/n) = Upper and lower confidence limit

95% confident that the true mean lies between the LCL and UCL