What is the confidence interval if the sample size is 30 instead?

[finalight]

Homework Statement

In a primary school, the mean height of the students of primary 1 students is 120cm. Given a sample size of 40, the confidence interval is 117 and 123. Find the confidence interval if the sample size is 30 instead.

Homework Equations

Standard deviation and confidence level is not given in this question

The Attempt at a Solution

It's a test, so I just gave it up due to not enough time to attempt to it. Test paper aren't given back, but I remember the question in details.

However i ask my one of my classmate and his solution was 120 +- x/[sqrt(40)/sqrt(30)] though the reason he told was like rocket science to me

 

[I like Serena]

Homework Statement

In a primary school, the mean height of the students of primary 1 students is 120cm. Given a sample size of 40, the confidence interval is 117 and 123. Find the confidence interval if the sample size is 30 instead.

Homework Equations

Standard deviation and confidence level is not given in this question

The Attempt at a Solution

It's a test, so I just gave it up due to not enough time to attempt to it. Test paper aren't given back, but I remember the question in details.

However i ask my one of my classmate and his solution was 120 +- x/[sqrt(40)/sqrt(30)] though the reason he told was like rocket science to me

Welcome to PF, finalight!

Do you have a formula for the calculation of a confidence interval?
From it, you can deduce the effect on the confidence interval if the sample size changes.

There is an assumption in your problem statement however.
Apparently it is assumed that the standard deviation of the sample of 40 is the same as the standard deviation of the sample of 30.

 

[finalight]

yes, i also assume that the standard deviation and the confidence level remain the same

however, even with the given formula, i still do not know how to calculate the result, because there are two unknowns; the confidence level and the standard deviation itself

 

[I like Serena]

If you write down the formula for n=30 and also for n=40, you'll see that they have a part in common.
You need to make use of that.

Can you perhaps write down your formula?

 

[finalight]

the general formula would be

mean +- confidence level * standard deviation/sqrt(sample size)

120 +- x * s/sqrt(40) = 117,123
120 +- x * s/sqrt(30) = ?,?

that's what i got, still can't see the similarity, except for the two unknowns there

unless you want me to use simultaneous equation...

 

[I like Serena]

Let's give x * s another name.
Let's call it A=x * s.

So your first equation (only the lower bound) is:
120 - A/sqrt(40) = 117

Can you solve A from this equation?
And then substitute the result in your second equation?

 

[finalight]

so that means

120 +- A/sqrt(30) = 117,123
-----------------------------------
Equation 1: 120 - A/sqrt(30) = 117

Equation 2: 120 + A/sqrt(30) = 123

are you referring to something like that?

 

[I like Serena]

I meant you to substitute the solution for A into:
120 +- A/sqrt(30) = ?,?

Then you get the result you want (the question marks).

Can you solve A from equation 1?
Equation 1: 120 - A/sqrt(30) = 117

Or from equation 2, which should give you the same result?