Normal hypothesis testing

Hello-
Something has really been confusing me lately- I'm not sure why Z values are in the markschemes for many hypothesis tests. (BTW I do AQA A level Maths)
and definitely how they work - where are they getting critical Z values from?
Also- how do you remember when to reject/accept based on the significance level? (esp for pmcc)

For example:
H0: µ = 66.5 H1: µ < 66.5
Z = −1.42
Critical z value = −1.28
−1.42 < −1.28
Reject H0 − there is sufficient evidence that the advertising campaign has reduced the consumption of chocolate.

Reply 1

mqb2766

Original post

by 2655AL-

Hello-
Something has really been confusing me lately- I'm not sure why Z values are in the markschemes for many hypothesis tests. (BTW I do AQA A level Maths)
and definitely how they work - where are they getting critical Z values from?
Also- how do you remember when to reject/accept based on the significance level? (esp for pmcc)
For example:
H0: µ = 66.5 H1: µ < 66.5
Z = −1.42
Critical z value = −1.28
−1.42 < −1.28
Reject H0 − there is sufficient evidence that the advertising campaign has reduced the consumption of chocolate.

The z values corresond to a normalised normal distrubtion, so subtract the mean and divide by the standard deviation (zero mean, unit standard deviation). Then z represents the number of standard deviations from the mean. So +/-2 standard deviations from the mean corresponds to the critical value that would represent a two tailed 95% confidence test. Or the critical z value corresponds to looking up the normalised (z) value which corresponds to the limits of the conidence region, so each 2.5% cumulative tail corresponds to the critical z values of +/-2.

There sholud be a few examples in your textbook? Sketching a normal distrubtion and marking/shading the tails which corresponds to the confidence limits/critical region should make it clear?