Hypothesis testing with critical values

1. A driving school has records showing that, over a long period, 72% of its students passed their test on the first attempt. Under a new management, some of the procedures have changed and they want to find out whether the pass rate has changed.

The hypotheses are tested using a random sample of 50 students. It is decided that the null hypothesis should be accepted if between 30 and 40 (inclusive) of the students pass the test on the first attempt.

a) State the critical region for the test

b) Find the probability of incorrectly rejecting the null hypothesis. What can be said about the significance level of the test.

Any help is appreciated!

Reply 1

artful_lounger

Universities Forum Helper

21

Please remember that the study help forum is not here to do homework for students and they will only provide feedback on your attempts at the solution and hints at guiding you to the correct answer. So please include your working so far and any thoughts on next steps if you are stuck, so the study helpers can assist you :smile:

Reply 2

username6583999

OP

2

Original post by artful_lounger

Please remember that the study help forum is not here to do homework for students and they will only provide feedback on your attempts at the solution and hints at guiding you to the correct answer. So please include your working so far and any thoughts on next steps if you are stuck, so the study helpers can assist you :smile:

Hi, I'm sorry I've only been able to write out the hypotheses and am completely stuck on where to go from there.

Here is what I have written so far:
H0: p=0.72
H1: p ≠ 0.72
p= proportion of students who pass the drivers test their first time.

X= number of students who pass the drivers test their first time
X~B(50,0.72)

However I'm stuck on where to go from here as we haven't been given a significance level (i think).

Thank you.

(edited 10 months ago)

Reply 3

mqb2766

21

Original post by kghj

Hi, I'm sorry I've only been able to write out the hypotheses and am completely stuck on where to go from there.

Here is what I have written so far:
H0: p=0.72
H1: p ≠ 0.72
p= proportion of students who pass the drivers test their first time.

X= number of students who pass the drivers test their first time
X~B(50,0.72)

However I'm stuck on where to go from here as we haven't been given a significance level (i think).

Thank you.

Youre asked to state the critical region and the numbers are given in the question.

Hypothesis testing with critical values

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