If you used Clearing in 2024, how did you find it?

Hypothesis testing

HI in the method I learnt for hypothesis testing, when doing critical region we divide the significance level by 2 then compare the lower tail value with that but for this question, it seems to be different, they compare the probability with the 1% instead of dividing it by 2 to get 0.5%, can anyone explain why they didn't compare with the 0.5% please?

3. It is known that on average 85% of seeds of a particular variety of tomato will germinate.
Ramesh selects 15 of these seeds at random and sows them.
i.
A. Find the probability that exactly 12 germinate.
[3]
B. Find the probability that fewer than 12 germinate.
[2]
The following year Ramesh finds that he still has many seeds left. Because the seeds are now
one year old, he suspects that the germination rate will be lower. He conducts a trial by
randomly selecting n of these seeds and sowing them. He then carries out a hypothesis test
at the 1% significance level to investigate whether he is correct.
ii. Write down suitable null and alternative hypotheses for the test. Give a reason for your
choice of alternative hypothesis.
[4]
iii. In a trial with n = 20, Ramesh finds that 13 seeds germinate. Carry out the test.
[4]

ALTERNATIVE METHOD – follow method above unless some mention of CR seen
Critical region method
LOWER TAIL

iv P(X ≤ 13) = 0.0219 > 1%
iv P(X ≤ 12) = 0.0059 < 1%
iv So critical region is {0,1,2,3,4,5,6,7,8,9,10,11,12}
iv 13 not in CR so not significant A1* Do not allow just ’13 not in CR’
iv
There is insufficient evidence to indicate that the proportion of seeds which have
germinated has decreased.

Reply 1

mqb2766

As they say, theyre only comparing the lower tail as its a <= test.

Reply 2

flutterbymanor

Original post by Disha2504

HI in the method I learnt for hypothesis testing, when doing critical region we divide the significance level by 2 then compare the lower tail value with that but for this question, it seems to be different, they compare the probability with the 1% instead of dividing it by 2 to get 0.5%, can anyone explain why they didn't compare with the 0.5% please?
3. It is known that on average 85% of seeds of a particular variety of tomato will germinate.
Ramesh selects 15 of these seeds at random and sows them.
i.
A. Find the probability that exactly 12 germinate.
[3]
B. Find the probability that fewer than 12 germinate.
[2]
The following year Ramesh finds that he still has many seeds left. Because the seeds are now
one year old, he suspects that the germination rate will be lower. He conducts a trial by
randomly selecting n of these seeds and sowing them. He then carries out a hypothesis test
at the 1% significance level to investigate whether he is correct.
ii. Write down suitable null and alternative hypotheses for the test. Give a reason for your
choice of alternative hypothesis.
[4]
iii. In a trial with n = 20, Ramesh finds that 13 seeds germinate. Carry out the test.
[4]
ALTERNATIVE METHOD – follow method above unless some mention of CR seen
Critical region method
LOWER TAIL
iv P(X ≤ 13) = 0.0219 > 1%
iv P(X ≤ 12) = 0.0059 < 1%
iv So critical region is {0,1,2,3,4,5,6,7,8,9,10,11,12}
iv 13 not in CR so not significant A1* Do not allow just ’13 not in CR’
iv
There is insufficient evidence to indicate that the proportion of seeds which have
germinated has decreased.

you only need to divide the significance level by 2 if it’s a two-tailed test (eg. when the alt hypothesis is ≠) but as you already know it’s lower tail, this is a one-tailed test so you don’t divide it