Question

A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and σ = 18. This sample mean corresponds to a z-score of z = –1.00.

Answer 1

True

Explanation:

Given that:

M = 27, sample of n = 36 scores, µ = 30 and σ = 18.

The z score is used in statistics to determine by how many standard deviations the raw score is above or below the mean. If the z score is positive, the raw score is greater than the mean and if the z score is negative the raw score is less than the mean. The z score is given as:

`z=(x-\mu)/(\sigma)`

Given that M = 27, this means that x = 27. Therefore:

`z=(x-\mu)/(\sigma)\\\\for \ a\ sample\ size(n):z=(x-\mu)/(\sigma/√(n) )\\\\z=(27-30)/(18/√(36) ) =(-3)/(3)=-1`

This sample mean corresponds to a z-score of z = –1.00.