This video explains how to do this sort of thing well.
But basically, you need to set up your hypothesis: XβΌPo(Ξ»)
H0: Ξ»=2 H1: Ξ»ξ =2
You will reject H0 if
Unparseable latex formula:
\mathbb{P}(X \leq x_{\ell}}) \leq 0.025
so you need to lookup this value of xββ in your table.
You will also reject H0 if P(Xβ₯xuβ)β€0.025 so you need to re-arrange this and get something like P(Xβ€xuββ1)β₯0.0975 and use the tables again to find this value of xuβ.
Your critical value is the interval of X s.t if X=x where x is in your critical interval, you reject H0, i.e: it will be [xuβ,xββ]
The tables will give approximately 0.025 and approximately 0.0975 so you'll select those but the actual significance level will be the probabilities from the table added together. (The video should explain it really well)
Nah, part (b) is asking you to deal with Ξ»=2 and Ξ»ξ =2, not X ~ Po(60), so no need for approximations.
But I need a sample statistic and the question says 'To test this, the number of cups of tea sold during a random 30 minute interval is recorded'. I can't see where else in the question this will be used.
But I need a sample statistic and the question says 'To test this, the number of cups of tea sold during a random 30 minute interval is recorded'. I can't see where else in the question this will be used.
Your sample statistic is XβΌPo(Ξ») where Ξ»=2 or
Unparseable latex formula:
\lambad \neq 2
.
Part (b) explicitly states the fact that you're testing the "rate of every 2 minutes".
You use the 30 minute interval thingy in part (b) as part of your explanation. Nowhere else.
You've computed Ο earlier so you just need to note that 2βΟ<X<2+Ο is an interval whose width is larger than the IQR width. The IQR width has probability 0.5 by definition (75% - 25% = 50%) so since the given interval is larger than the IQR then the probability of that interval is larger than the probability of the IQR so the probability is greater than 0.5. Let me know if you need a clearer explanation, seriously - there's no problem if you need to clarify something, you seem to never to and I don't know if that's because you understand it all or...
You've computed Ο earlier so you just need to note that 2βΟ<X<2+Ο is an interval whose width is larger than the IQR width. The IQR width has probability 0.5 by definition (75% - 25% = 50%) so since the given interval is larger than the IQR then the probability of that interval is larger than the probability of the IQR so the probability is greater than 0.5. Let me know if you need a clearer explanation, seriously - there's no problem if you need to clarify something, you seem to never to and I don't know if that's because you understand it all or...
Thank you, I see what you mean how the IQR probability is 0.5 always but how do we work out its width in this question? Haha yeah normally you give me the eureka breakthrough, but this question has got me particularly stumped!
Thank you, I see what you mean how the IQR probability is 0.5 always but how do we work out its width in this question? Haha yeah normally you give me the eureka breakthrough, but this question has got me particularly stumped!
In this case the distribution is symmetric - so, since the lower quartile is at 1.41 = (2-0.59) then the upper quartile will be at 2 + 0.59 = 2.59. SO the IQR is [1.41, 2.59]
Whereas the interval given is is [1.184, 2.816]. i.e: you should be able to see how the intervals are always 2-something to 2 + something given that the graph of the distribution is symmetric about the line x=2. So really you don't need to compute 2 + 0.59 = 2.59; it's enough to note that 2-0.816 < 1.41 so the given interval is larger than the IQR.
In this case the distribution is symmetric - so, since the lower quartile is at 1.41 = (2-0.59) then the upper quartile will be at 2 + 0.59 = 2.59. SO the IQR is [1.41, 2.59]
Whereas the interval given is is [1.184, 2.816]. i.e: you should be able to see how the intervals are always 2-something to 2 + something given that the graph of the distribution is symmetric about the line x=2. So really you don't need to compute 2 + 0.59 = 2.59; it's enough to note that 2-0.816 < 1.41 so the given interval is larger than the IQR.
followed by the distribution x (squiggle) N or B or lambda (distrubution)
?
No but I would write down the x (squiggle) N or B or Po (distrubution) so that they know what you were intending to use in case you look up the wrong number. There is often a mark for "evidence of using ...... distribution".