Standardising the Test Statistic in Hypothesis Testing

The video tutorial explains how to standardize test statistics using the normal distribution. It covers the calculation of Z-values and the concept of rejection regions for hypothesis testing. An example is provided using test scores of Year 13 students to demonstrate hypothesis testing at a 5% significance level. The tutorial also explores a one-tail test to determine if Year 13 students performed better. Finally, it introduces potential errors in hypothesis testing.

What is the formula used to calculate the z-value in a normal distribution?

• x bar plus the mean times the variance

• x bar minus the mean times the standard deviation

• x bar plus the mean divided by the variance

• x bar minus the mean divided by the standard deviation

What z-values define the rejection region for a two-tail hypothesis test at a 5% significance level?

• -2.58 and 2.58

• -2.33 and 2.33

• -1.65 and 1.65

• -1.96 and 1.96

What does a two-tail hypothesis test at a 5% significance level imply about the rejection region?

• 10% on either side of the distribution

• 1% on either side of the distribution

• 2.5% on either side of the distribution

• 5% on either side of the distribution

In the context of the student logic test, what was the calculated z-value?

• 1.96

• 1.645

• 2.33

• 1.792

What was the decision regarding the null hypothesis for the year 13 students' performance?

• Reject the null hypothesis

• Data was inconclusive

• Do not reject the null hypothesis

• Not enough information to decide

What critical value is used when testing if year 13 students performed better than average?

• 1.645

• 1.96

• 1.792

• 2.33

What does a z-value of 1.792 indicate about year 13 students' performance compared to the critical value of 1.645?

• Insufficient evidence to suggest better performance

• Sufficient evidence to suggest better performance

• Data is inconclusive

• Indicates worse performance

How does changing the hypothesis from 'not equal to' to 'greater than' affect the test outcome?

• It changes the rejection region

• It does not affect the outcome

• It lowers the significance level

• It requires a larger sample size

What is the impact of adjusting the values in hypothesis testing?

• It can change whether the null hypothesis is accepted or rejected

• It has no impact on the results

• It only affects the type of statistical test used

• It changes the data distribution

What potential errors can occur in hypothesis testing?

• No errors can occur

• Sampling errors and calculation mistakes

• Only calculation mistakes

• Only sampling errors