- 00:03
[Testing One Sample Mean]

- 00:09
NARRATOR: Let's evaluate the mean of a sampleby determining the probability of getting the sample mean.We determine this probability by transforming the sample meaninto a statistic, known as t, and placing itin a distribution of t statistics.If we look at the two formulas z and t,we'll see that they look a lot alike.

- 00:31
NARRATOR [continued]: The numerator involves the difference between somethingand the population mean, mu, and the denominatoris a measure of variability.For z scores, the denominator is the variability of scores.For the t statistic, the denominatoris a measure of variability, not of scores, but of sample means.

- 00:51
NARRATOR [continued]: The variability of sample means is a tricky concept.In order to understand what the denominator of this formula is,we need to describe another distribution, knownas the sampling distribution of the mean.Let's start with whether or not to reject the null hypothesis.What does this mean?We want to decide whether the sample

- 01:12
NARRATOR [continued]: mean is significantly different than the population mean, mu.We do this by determining the probabilityof getting our value of the sample mean given allpossible values of the sample mean.This may sound new, but this is similar to determiningthe probability of a score x given all possible scores.So to determine the probability of a sample mean,

- 01:33
NARRATOR [continued]: we need a distribution of all possible sample means.This is the sampling distribution of the mean.Let's say we have a variable with the population mean mu.For example, imagine the average IQ in a population is 100.We draw a random sample of the population,and then we calculate the mean IQ.

- 01:54
NARRATOR [continued]: We'd expect the sample mean to be 100.Given the influence of random chance factors,the sample mean could be more than 100 or less than 100.So we continue this process and draw another samplefrom the population and calculatethe mean of that sample.It might be 100, or it might not.Imagine doing this an infinite number of times.

- 02:16
NARRATOR [continued]: We draw an infinite number of samplesand calculate an infinite number of sample means.The distribution here would look like a normal distribution.In the middle is the mean.In this case, it would be mu.But this distribution has variability.We represent variability with a standard deviation.So now we need a standard deviation, not of scores,

- 02:40
NARRATOR [continued]: but a standard deviation of sample means.That's the standard error of the mean.If we went out 1 and minus 1 standard deviations,this would not be the standard deviation of scores.It's the standard deviation of sample means.That's a standard error of the mean,and that's the denominator of the formula for t.

- 03:01
NARRATOR [continued]: It represents the variability of sample means.This video involves testing hypotheses about a population,stating a value for a population mean.But it's possible there could be research situations wherethe population mean is not known.In these situations, the goal is notto test the hypothesis regarding a population mean,

- 03:22
NARRATOR [continued]: but to estimate what we believe the population mean might be.That's what we'll focus on next.

### Video Info

**Publisher:** SAGE Publications, Inc.

**Publication Year:** 2019

**Video Type:**Tutorial

**Methods:** Sampling, Standard error, Standard deviations, Sampling distribution

**Keywords:** mean (of a population); Statistical and measurement terms; variance (of a population)

### Segment Info

**Segment Num.:** 1

**Persons Discussed:**

**Events Discussed:**

**Keywords:**

## Abstract

An explanation is given for how to determine the probability of getting the value of the sample mean given all possible values of the sample mean.