A large school board is considering introducing a new teaching method for math. They are concerned that currently only 65% of the their students pass the provincial exam and want to improve the situation. They decide to use the new method for this year's 4000 grade 12 students. If there is evidence at the 5% significance level of an improvement in the pass rate, they will introduce the new method for all grade 12 students in the future. We will consider this year's Grade 12 students to be representative of Grade 12 students at the school in other years.

Worksheet 1: Minitab output

Test and CI for the One P

Method

p: event proportion

Normal approximation method is used for this analysis

Descriptive Statistics

95% Lower Bound

N Event Sample p for p

4000 2660 0.665000 0.652725

Test

Null hypothesis Ho:p=0.65

Alternative hypothesis H1:p>0.65

Z-Value P-Value

1.99 0.023

For each of the assumptions needed to carry out the hypothesis test listed below, state the condition needed to verify each and show that they have been met in the context of this question

1) Independence Assumption: the randomization condition is not met, since the question states they are using the method on this year's grade 12 students.

Discuss plausible independence in the context of the problem (is it reasonable to consider the independence assumption is met, even without taking a random sample?)

2) Check the sample size assumption

3) State the appropriate hypothesis (Ho and Ha) in symbols and define the parameter in context

4) Identify the test statistic and p-value from the minitab output

z=

P-value=

5) Briefly asses the significance of the evidence. Justify your answer

6) State your conclusion in the context of the problem