s2~hypothesis test

7

In an experiment, there are 250 trials and each trial results in a success or a failure.

It is claimed that 10% of students can tell the difference between two brands of baked beans. In a random sample of 250 students, 40 of them were able to distinguish the difference between the two brands.

(b) Using a normal approximation, test at the 1% level of significance whether or not the claim is justified. Use a one-tailed test. (6)
(c) Comment on the acceptability of the assumptions you needed to carry out the test.(2)

i have never seen such a question, could someone help me out plizz

Reply 1

Simba

16

Try it using the normal approximation X ~ N[np, np(1 -p)] :smile:

...

Reply 2

Loz2402

TEE001

In an experiment, there are 250 trials and each trial results in a success or a failure.

It is claimed that 10% of students can tell the difference between two brands of baked beans. In a random sample of 250 students, 40 of them were able to distinguish the difference between the two brands.

(b) Using a normal approximation, test at the 1% level of significance whether or not the claim is justified. Use a one-tailed test. (6)
(c) Comment on the acceptability of the assumptions you needed to carry out the test.(2)

i have never seen such a question, could someone help me out plizz

Let X be the number of students who can tell the difference between two brands of baked beans.
X ~ B(250, 0.1)

This can be approximated using the normal approx.
Y ~ N(np, np(1-p))
Y~ N(25, 22.5)

H0: p=0.1
H1: (not sure here, i would have used a 2-tailed, but they say one...)
is this where you got stuck?
would you just have to use H1: p < 0.1? hmmm...

Reply 3

singh12

They have given a clue in the question. The question says, test at the 1% level of significance whether or not the claim is justified. If the claim is justified then you have to use < for the probability.

Reply 4

TEE001

OP

7

the thing is i have never done a hypothesis testing question which involves normal approximation, which values am i comparing to see the significance??

Reply 5

singh12

Try using P(X<) if the answer is less than 0.01 then it is significant...

Reply 6

TEE001

OP

7

oh, thanks alot. i understand it now--

s2~hypothesis test

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