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

7) What type of error could we have made here, Type I or Type II? Explain in context

8) Calculate the estimated effect

size and interpret this value in context

9) Calculate a 95% confidence

interval for this data (you do not need to interpret the interval). Keep as

many places after the decimal as possible while doing your calculations. Enter

your final answer only, rounded to 4 decimal places. Do not change your answer

to percent

(______,_______)

10) Based on the confidence

interval, what can you conclude about the hypothesis? Explain briefly

Choose which words fit best in the

sentence:

We would either: Reject Ho/Not

reject Ho/Conclude Ho

since: 0.665 or 0.65

is: In or not within

the range or the interval

11) Implementing the new method

will be expensive. Based on the interval, assess the practical significance of

introducing the new method.