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S3 Help!!

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Hiya , I’m quite stuck on part C of question three and maybe it’s because I don’t really understand the assumptions but one of the answers was for C is about how the sample size has to be large enough to use the central limit theorem but I am confused because I thought the sample size is 10 and that’s not really large so why would we have to involve the central limit theorem?

Thank you
Original post by Angels1234
https://postimg.cc/image/6i59tgmf1/

Hiya , I’m quite stuck on part C of question three and maybe it’s because I don’t really understand the assumptions but one of the answers was for C is about how the sample size has to be large enough to use the central limit theorem but I am confused because I thought the sample size is 10 and that’s not really large so why would we have to involve the central limit theorem?

Thank you


Did you use the sample size of 10 for part b then?
In part (b), when you worked out the 95% confidence interval you used the central limit theorem which let you assume that the sample mean follows a normal distribution. You need a sufficiently large sample size for the central limit theorem
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Angels1234
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Original post by ghostwalker
Did you use the sample size of 10 for part b then?


Omg !! Silly me , thanks so much 😂 100 not 10
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Original post by Bealzibub
In part (b), when you worked out the 95% confidence interval you used the central limit theorem which let you assume that the sample mean follows a normal distribution. You need a sufficiently large sample size for the central limit theorem


Why do the confidence interval formulas involve the central limit theorem ? @ghostwalker @Bealzibub ??For example if we are told n is 20 and we used that to find the confidence interval for example in 95 % ci that n value is small so why does that involve clt ?
Original post by Angels1234
Why do the confidence interval formulas involve the central limit theorem ? @ghostwalker @Bealzibub ??For example if we are told n is 20 and we used that to find the confidence interval for example in 95 % ci that n value is small so why does that involve clt ?


The confidence interval formula is for a normal distribution. When you take a sample and calculate its mean, how do you know what distribution the sample mean is, how can you calculate a confidence interval if you don't know the distribution? This is where the central limit theorem comes in, the theorem says that regardless of the distribution from which you sample, the sample mean will be approximately normally distributed as long as the sample size is sufficiently large. You can then calculate the confidence interval, so when you use the confidence interval formula you are actually using the central limit theorem!

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