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As mathematics statistics hypothesis testing

It is known from past records that 1 in 5 bowls produced in a pottery have minor defects. To monitor defects.To monitor production a random sample of 25 bowls was taken and the number of such bowls with defects was recorded.
A) using a 5% level of significance, find critical regions for a 2-tail test of the hypothesis that 1 in 5 bowls have minor defects. The probability of rejection, in either tail, should be no more than 2.5%?
B) state the actual significance level of the above test?

Reply 1

Man_Like_$

So u want the answer?

Reply 2

Jake.f16

Original post by Man_Like_$

So u want the answer?

Yes please

Reply 3

Jake.f16

Original post by Jake.f16

Yes please

Im really struggling I need some help or advice

Reply 4

number0

I would first get the tables of cumulative binomial distribution up, found here https://goo.gl/TWxkow. Can you see how in this case you will be using X - B(25,0.2) as your binomial distribution. Then use the tables to find the values of x with probability less than, but as close to, 2.5% for both ends of this test. It's quite hard to explain in words.

Reply 5

Notnek

Original post by number0

Be aware that some schools won't be teaching using tables anymore and certain tables won't be available depending on the spec. Calculators will be used more for the new spec.

Original post by Jake.f16

Can you please tell us what you've tried so far and if you have been taught to do this using your calculator or tables?

Reply 6

number0

Original post by Notnek

Be aware that some schools won't be teaching using tables anymore and certain tables won't be available depending on the spec. Calculators will be used more for the new spec.

Can you please tell us what you've tried so far and if you have been taught to do this using your calculator or tables?

I remember doing this question with my edexcel spec, so i just assumed he was doing this spec aswell. Could be wrong tho. And tbh i think the tables are a lot faster and more simple way of doing these questions but thats just me

Reply 7

Notnek

Original post by number0

If you're used to the new calculator then using it for these kinds of questions will be faster than using tables. Some teachers will teach the new spec only using a calculator and without tables. For normal distribution you have to use the calculator for certain questions.

In my personal opinion the use of a calculator is better because using tables is very old fashioned.

Reply 8

number0

Original post by Notnek

I agree for most cases the calculator is better but for this specific question where you find the critical values if you use the calculator you waste time just guessing values until you find the correct one, taking up time randomly putting values in, whilst with the tables you can just scroll through until you find easily the probability wanted for each end of the test.

Unless i am missing something and you dont have to just guess to find the critical value on the calculator

Reply 9

Notnek

Original post by number0

It's not a random guess since 1 in 5 implies that the expected number of defects will be 5. So you check values around 5. It took me a few seconds after I got into the correct mode.

It's just my opinion but I'm a fan of trying to do every question using the calculator because you will get more practice and it means you can stick to one method instead of using both tables and calculator.

Reply 10

number0

Original post by Notnek

But you still then have to find the upper critical value, which is surely undeniably better with the tables. Love me a good debate on statistical tables.

Reply 11

number0

But it is each to their own, don't really know why im still arguing, just bored rly

Reply 12

Notnek

Original post by number0

But you still then have to find the upper critical value, which is surely undeniably better with the tables. Love me a good debate on statistical tables.

You have to find a probability above 0.975 which is just as fast as finding the lower value. A lot of teachers would argue with me but I'm just a calcualtor fan. Thanks for the debate :smile: