# Confidence Intervals Flashcards

What is a point estimate?

is a single value estimate of a population parameter e.g. a sample mean

What is an interval estimate?

a range of possible values of a population parameter: e.g. a confidence interval

What does a confidence interval (CI) describe?

A confidence interval (CI) describes an interval (i.e. a range) of values for our population parameter, together with a specified level of confidence that the parameter is in that range

When given the question: • How big should the range be for us to have 95% confidence that it contains pop mean? what should you consider to work this out and what does this mean (remembering that we are interested in a sample mean and its relation to the population mean) (we have the sample statistics and the population standard deviation but not the population mean)

- sensible to consider the sampling distribution of the mean
- the SDM is normal so a z-transformation can take place
- the area under the SND between z= -1.96 and z = 1.96 is 0.95 (95%)
- therefore 95% of our z-scores are within 1.96 standard deviations of the population mean
- and if we repeated our data collection many times then 95% of sample means would be within 1.96 standard errors of the population mean

What is the equation that says that 95% of sample means would be within 1.96 standard errors of the population mean?

u - (1.96 x standard error) to u+ (1.96 x standard error)

If 95% of our sample means would be within 1.96 standard errors of our population mean what else does this mean?

- That 95% of our population means would be within 1.96 standard errors of our sample mean
- therefore 95% of repeats would be within:
- m – (1.96 x standard error) to m +(1.96 x standard error)

What is the basic principles of confidence interval theory?

- For a sample size of size N drawn from a random from a normal population N(u, standard deviation) with known s.d.:
- The 95% CI for the population mean is centred on the sample mean mm and goes from m- (1.96 x standard error) to m +(1.96 x standard error)
- C.I lower = -1.96 standard errors
- C.I upper = + 1.96 s.e.s
- A 95% confidence level means that if we repeated our sampling many times and worked out a new CI each time that was centred on our new sample mean we would expect the population mean to be in that interval on 95% of repeats

Calculate the confidence intervals at 95% for a sample size of 15 with population parameters: N(?,8.9) and sample statistics: N(163.2,14.3)

- we can work out our standard error: 8.9/square root 15 = 2.30
- for 95% repeats u would be within 1.96 standard errors of m:
- m -(1.96 x s.e) to m +(1.96 x s.e.)
- 163.2 - (1.96 x 2.3) to 163.2 + (1.96 x 2.3)
- C.I. lower = 163.2 - (1.96 x 2.3) = 158.69
- C.I. upper = 163.2 + (1.96 x 2.3) = 167.71
- 95% C.I = (138.69, 167.71)