Sample Tests

Question 1

What types of Hypotheses are there?

Answer 1

• The statistical hypotheses are set up as two options (H0 and H1), but H1 is also known as HA

Question 2

What is the difference between (H0 and H1) of a Hypotheses?

Answer 2

• H0 and H1 have to cover every possibility
• The Null Hypothesis (Ho) has to state that nothing has happened- the status quo - this is what we will accept unless the data shows otherwise
• The Alternative Hypothesis (H1 or HA) has to cover everything else

Question 3

What are some characteristics of the Null hypotheses?

Answer 3

• It is always the hypothesis that we want to disprove
• It is usually opposite to what the researcher wants to prove
• It is stated in terms of population parameters

Question 4

What types of tests can we have when setting up a hypotheses?

Answer 4

• One or two tailed tests

Question 5

What is two tailed testing?

Answer 5

Two tailed testing: Non directional hypothesis

• H0: the means are equal
• H1: the means are not equal

Question 6

What is one tailed testing?

Answer 6

One tailed testing: Directional hypotheses

• H0: Nothing changed
• H1: Less or greater than

Question 7

Study the example of Two Tailed Testing

Answer 7

• If we are interested in the effect of two different soils on the growth rate of plants
• Hypotheses (English): the H0 is that there is no difference in the population mean growth rate of plants
• The H1 will state that there was a difference
• Hypotheses (Symbols):
  H0: μ = μ
  H1: μ does not = μ

Question 8

Study the Example of One Tailed Testing

Answer 8

• Is the NOX in the atmosphere increasing from time 1 to time 2?
• Hypotheses (English): H0: The population NOX levels either stayed the same or decreased from time 1 to time 2 (ie: they did not increase). H1: The NOX levels increased from time 1 to time 2
• Hypotheses (Symbols):
  H0: μ1 > μ2
  H1: μ1 < μ2

Question 9

What is a decision rule?

Answer 9

• A formal rule that states, based on the data obtained, when to reject the null hypothesis H0

Question 10

What is a test statistic?

Answer 10

• A statistic used in statistical hypothesis testing

Question 11

What does the Decision Rule depend on?

Answer 11

• Depending on where our Test statistic (which we will be calculating later) falls within the sampling distribution, we will be rejecting or accepting H0

Question 12

What are the seven components of a hypotheses test?

Answer 12

• H0 (What the researcher is investigating)
• H1 or HA (Alternate Hypotheses; your research question; what you are trying to show)
• α (significance level; when do we reject the null hypotheses
• dR (Decision Rule; Where we use the α to get the value for our decision)
• ts (Test Statistic; is a formula)
• tsv (Test statistic value; point estimate; another formula)
• con (Conclusion; where we take the tsv and compare it to our decision rule

Question 13

What is a hypotheses test?

Answer 13

Question and ask whether we have the evidence to suggest something has changed or something is different

Question 14

What does it mean when the null hypotheses is rejected?

Answer 14

• This means that the Null Hypotheses is no longer correct

Question 15

What are the two different types of one sample tests?

Answer 15

• One sample z test

- One sample t test

Question 16

How do you know which one sample test to use?

Answer 16

There is a rule in statistics that states:

• Whenever you have σ you always use the z test
• Whenever you have S you always use the t test

Question 17

What does every test in statistics have?

Answer 17

• Assumptions

- In every part of statistics there is some level of unknown that should be there so that the data can be numerical

Question 18

What are some examples of assumptions for z tests?

Answer 18

• Underlying population distribution is a Normal distribution
• Samples are independent and random observations

Question 19

What is assumed about the model in z tests?

Answer 19

• Every sample observation can be modelled
• The model consists of a determined (explained) component and a random (unexplained) component
• Each obs. = grand mean + sample effect + random
  variation

Question 20

What can a “one sample t test” test?

Answer 20

• If the population mean is equal to a set value: Two tailed test.
• If the population mean is greater (or smaller) than a set value: One tailed test

Question 21

What are some assumptions that need to be made for a t test?

Answer 21

• The observations in the sample should be random and independent (sampled without bias).
• The population distribution is a Normal distribution - the test is reasonably robust to departures from this assumption

Question 22

What happens to the t test if n is larger than 30?

Answer 22

• If n, and therefore df, is large (> 30) then a Normal distribution can be used instead of a t-distribution

Question 23

Study the process for finding the test statistic in a t test

Answer 23

https://docs.google.com/document/d/1r_ttbYs-4jXdkBbVGPH9vk1swjRRmRJUWdllcJXdaAI/edit?usp=sharing

Question 24

What should a t Test conclusion have?

Answer 24

• You should always state the conclusion in plain English (no statistical jargon).
• You should state the probability associated with your conclusion.
• Example - For a two tailed test: The DO in the stream was significantly (p < 0.05 or
  p = 0.002) different than 3.
• Example - For a one tailed test: The species richness for the rain forest site is not significantly (p > 0.05 or p = 0.210) higher than 150