Confidence intervals, p-values

[Lucy de Faoite]

Hi there, 

My 6th HL students are doing hypothesis test Qs atm from the papers. Two of the more recent marking schemes have confused me. In 2020 8c, the marking scheme only seems to accept a z-score method. It mentions that a formulated confidence interval would only gain 4 out of 10 marks. I would have thought a confidence interval with a correct inference or the p-value should give full marks? 

In 2022 5b, a z-score method or confidence interval is accepted (no mention of p-value). I’m also a bit confused by the confidence interval solutions, I have taught it as x bar plus/minus 1.96 x standard error (to calculate the interval) and then see if the actual mean is in that range. The marking scheme sees if x bar is in the range (or alternatively, calculates mean plus/minus…. And sees if the mean is in the range). 

Hoping someone can help. 

Many thanks, 

Lucy de Faoite 

Gaelcholáiste Reachrann 

[Lucy de Faoite]

Apologies, 

I have re-read the solution for 2022 5b, and it’s fine. So my question is now just is p-value also accepted? 

Thanks 

[Stephen Lawless]

In general if z-score is accepted, then p-value should be accepted also. Afterall, there is a one-to-one relationship between them in the tables so surely any statement about one would be logically equivalent to the other?

As for the confidence interval, it should also be accepted. The 4 out of 10 would be for making the interval but not making any conclusions about it.

As the solutions always say "The model solutions for each question are not intended to be exhaustive – there may be other correct solutions" and I have no doubt solutions about p-value and CIs would be acceptable.