Further Statistics 1 - Poisson & Binomial Distributions - HELP

Hi all, how would I go about answering this question? I'm stuck with part (a); I'd be inclined to assume that the null hypothesis is p=9 and the alternative hypothesis is p<9, but p has to be smaller than 1 as it's a percentage.. Covered hypothesis testing in AS Level Stats, but never like this before so am completely lost!

Reply 1

confuzzledteen

Oops, image of question:

Screen Shot 2020-10-19 at 12.57.46 AM.png75.9KB

Reply 2

DFranklin

You say "... p < 9", but you haven't defined what p is.

[Not just being picky: I think you are confusing yourself by describing this as p].

Reply 3

confuzzledteen

Original post by DFranklin

You say "... p < 9", but you haven't defined what p is.

[Not just being picky: I think you are confusing yourself by describing this as p].

Hi, I think I've worked it out.. Basically, I was confused because I was doing this question like how I was taught for AS Level Mathematics (hypothesis testing for the binomial distribution), so I assumed that p was probability thus was confused as I didn't understand how probability could be a 9.

However, I've now realised that this question is actually asking for me to do hypothesis testing for a Poisson distribution. Makes no sense to me as this is Chapter 2 of the textbook (hypothesis testing for a Poisson distribution isn't till Chapter 4!) but I've just flipped to that chapter and it seems to fit the question. So I've tried and ended up with:

(a) Null hypothesis: λ=9
Alternative hypothesis: λ < 9
(b) assume null hypothesis is correct, so X~Po(9)
significance level 5%, hence requires P(X≤ c) < 0.05
looked at the tables..
P(X≤ 3) = 0.0212 & P(X≤ 4) = 0.0550
hence as P(X≤ 3) < 0.05, the critical value is 3 meaning that the critical region is X≤ 3
(c) actual significance level = P(X≤ 3) = 0.0212 = 2.12%
(d) Unsure what the question wants, I don't understand what the wording "comment on this observation in light of your answer to part b) means.. But I've gone ahead and written: X=4 does not lie in the critical region, so there is insufficient evidence to reject the null hypothesis. Hence, we can conclude that the engineer has not reduced the average number of errors.

As I don't have a markscheme (hence have no idea if I'm right or not), I was wondering whether you could double check if you're alright with that? Never done this before and have just tried to teach myself the concept so Idk if I'm right x

Reply 4

DFranklin

Havent checked the figures but the method looks fine (with caveat that it's getting on for 40 years since I did hypothesis stuff).

The one thing I'd say is that the conclusion should be: "we cannot conclude that the engineer has reduced...", not that we can conclude that he hasn't.

Reply 5

confuzzledteen

Original post by DFranklin

Alright, thank you so much!!

Reply 6

confuzzledteen

@DFranklin sorry to bother you! but you seem well-informed :smile:

i was just curious, for this question.. again, the wording has confused me. when it says "at least nine cars or vans".. does that mean like at least 9 vehicles (both cars and vans included)?

i've got Cars~Po(3.4) and Vans~Po(1.3),, so Cars & Vans~Po(4.7)
hence for the question,, find the probability that there will be at least nine cars or vans passing the recording point in a randomly selected 30 second interval, would i be finding P(Cars & Vans ≥ 0) ? I know the method, just unsure what the question actually wants haha

Further Statistics 1 - Poisson & Binomial Distributions - HELP

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you