Hypothesis Testing

Question 1

What is a null hypothesis?

Answer 1

The default position (H₀)
The original statement given in the question

Question 2

What is the alternative hypothesis?

Answer 2

The alternative possibility in respect to the null hypothesis (H₁)

Question 3

What is a one-tailed test?

Answer 3

A situation in which you are testing whether a parameter is more than or less than a value

Question 4

What is a two-tailed test?

Answer 4

A situation in which you are testing whether a parameter is not equal to a value

Question 5

How do you decide whether to accept/reject the null hypothesis?

Answer 5

If the data is within the critical region for the value stated, accept the null hypothesis
if the data falls outside of the critical region for the value stated, reject the null hypothesis and accept the alternative hypothesis

Question 6

What are the two methods for conducting a hypothesis test?

Answer 6

• Finding the critical region and comparing to the test statistic
• Finding the probability of being at least as extreme as the test statistic and comparing to the significance level

Question 7

How do you carry out the probability comparison method of hypothesis testing?

Answer 7

• Write out the hypotheses
• State the distribution being used for the test
• Draw the graph and shade
• Write a number line of X values
• Look up probability
• Compare probability and significance level
• Concluding statement

Question 8

How do you carry out the critical region comparison method of hypothesis testing?

Answer 8

• Write out the hypotheses
• State the distribution being used for the test
• Draw the graph and shade
• Write a number line of X values
• Construct a table of probabilities
• Compare critical region and test statistic
• Concluding statement

Question 9

What should you do if the probability of the test statistic < significance level?

Answer 9

Reject the null hypothesis
(There is enough evidence to suggest…)

Question 10

What should you do if the probability of the test statistic > significance level?

Answer 10

Accept the null hypothesis
(There is not enough evidence to suggest…)

Question 11

How do you find P(X is greater than or equal to A)?

Answer 11

1 - P(X is less than or equal to A-1)

Question 12

What do you do to the significance level if you are dealing with a two-tailed test?

Answer 12

Half it
10% significance level becomes 5% on each side

Question 13

Where is the expected value plotted on the bell curve?

Answer 13

At the peak of the curve (the centre)

Question 14

Where should the test statistic be plotted on the bell curve?

Answer 14

As the critical value
Then, test whether this is true

Question 15

What does the actual significance level of a test mean?

Answer 15

The probability of this test statistic falling in the critical region, assuming the null hypothesis is correct.
(if P = 0.02 so therefore 0.02 < 0.05 sig level, then the actual sig level is 2%)

Question 16

What is the acceptance region?

Answer 16

Any region of the bell curve which is not shaded
(Can be used in conclusions when accepting null hypothesis: ‘The test statistic lies within the acceptance region therefore accept the null hypothesis’

Question 17

What is the critical value?

Answer 17

The first value to fall inside the critical region

Question 18

For critical region hypothesis testing, how do you input data into calculator?

Answer 18

• Choose the list option in the calculator after going on binomial CD/PD
• List test statistics necessary in X column
• Press = and input n and p values
• Accept the first value which is in the critical region and write a statement

Question 19

When reading calculator probabilities for critical region hypothesis testing, how do you decide which value to accept for both less than or more than the H₀?

Answer 19

If you are looking for the critical value < H₀,
choose the first value below the significance level
(if sig level is 5%, first value below 0.05)
If you are looking for the critical value > H₀, choose the first value greater than 1 - significance level
(if sig level is 5%, the first value above 0.95)
Always +1 to the critical value for CV > H₀