Lecture 8- Hypothesis Testing 1

Question 1

What is inferential statistics?

Answer 1

Used to decide about the population based on observations of the sample

Question 2

What are the the parameters of a population?

Answer 2

They are the measures we are interested in

• Mean (μ)
• Standard deviation (σ)

Question 3

What word do we use instead of a parameter when talking about a sample? Give examples…

Answer 3

Statistic

These are the

• x (with line on top)= mean
• s= standard deviation

Question 4

What are the three steps for hypothesis testing?

Answer 4

1) Make a guess about the population frequency distribution – hypothesize what μ is
2) Take a random sample
3) Decide if sample came from a pop. like the one you guessed in step 1 (usually based on how close the sample mean is from the hypothesized population mean)

Question 5

Why is any sample likely to be naturally different from a population?

Answer 5

• sample based on fewer cases

- individuals vary individuals vary

Question 6

How do we tell if a difference in the sample mean and estimated population mean is due to variability or a true difference?

Answer 6

Central limit theory

Question 7

What is central limit theory?

Answer 7

Take lots of different samples of the same size. Take the individual means of each. Plot all the means in a frequency distribution (dot each time on the scale where get that mean). In the end it will pretty much look like a normal distribution. The more samples you take the more closely the sampling distribution will look like a normal distribution and the lower the standard deviation will be (spread less far out) . Therefore, we can assume that so long as our sample is big enough the means will resemble a normal distribution and we can use the normal things about normal distributions when making inferences.

Question 8

What are three features of a sampling distribution?

Answer 8

1) Normal
2) Has mean μ (the mean of the sampling distribution is equal to population mean)
3) Has standard deviation

Question 9

What is standard error in a sampling distribution?

Answer 9

Its the standard deviation of a sampling distribution.

Basically it’s a measure of how much the means differ from one sample to another.

Question 10

What does the variation in the size of the standard error of a sampling distribution tell us?

Answer 10

Large= lots of variability
Small= less variability 

With less variability is it more likely that the sample mean matches that of the population

Question 11

How do you calculate standard error?

Answer 11

An estimate can be made by taking the standard deviation of a single sample and dividing it by the square root of the number of observation in the sample

Question 12

What is the null hypothesis?

Answer 12

The first (conservative) hypothesis that you make. In other words you hypothesize that any difference in the true population mean and that of the experiment group is due to variability i.e not significant

Question 13

What is an alternative hypothesis?

Answer 13

The hypothesis that the treatment has had a real effect and difference in results in not just due to natural variability

Question 14

Do you ever ‘accept’ the null hypothesis?

Answer 14

No only retain

Question 15

What are you doing when you reject the null hypothesis?

Answer 15

Accepting the alternative hypothesis

Question 16

What is a significant level or alpha level?

Answer 16

The probability value that defines the boundary between rejecting or retaining the null hypothesis (Ho)

Question 17

What is the significance level often set at?

Answer 17

p less than .05 (sometimes .01)

Question 18

What’s the difference between a one-tailed and two-tailed t test/ when would you use them?

Answer 18

Two- tailed tests are more conservative and less powerful than one-tailed tests
Use two tailed test unless there is a “good” (e.g. theoretical) reason to use a onetailed
One-tailed is used when there is directional alternative. We have a belief that the experiment will have effect on the data in a certain direction (e.g. improve- scores go up)