STATS - samling distribution and confidence intervals

If a parent population is ND (μ, σ) then the sampling distribution of the mean is distributed ______ with mean ___ and SD ___

Distributed normally with mean μ and SD σ√N

Standard deviation of the mean sample distribution (or standard error of the mean)

σ√N

Confidence interval

An interval of values within a population parameter and the confidence that the parameter is within this range

When ND (μ, σ) has a known sample size (N) and SD, the 95% confidence interval for the population mean (μ) is centred on _____ within ______ standard errors of ____

Centred on sample mean (m) and within 1.96 standard errors of m

The IQ distribution of 11+ kids follows a normal distribution: N(130, 10). What is the standard deviation of the sampling distribution of the mean for samples from this population of size 16?

height h~ N(170, 14). You calculate the mean height of 173cm for a sample of 16 people from this distribution.

What is the standard error for samples of this size?

What is the z score of this sample mean?

height h~ N(125, 10).

What is the probability of selecting a sample of 25 people from this distribution with mean height less than 123

height h~ N(170, 14).

What is the probability of selecting a sample of 25 people from this population with mean height in the range from 171cm to 172cm

In a population the SD of heights is 3.2cm but, with unknown population mean/

In a random sample N=16 the mean sample height is 17.4

What is the 95% confidence interval for the population mean centred on the sample mean?