# Level 3 maths (core maths) confidence Intervals

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#1
When the blood pressure is measured two numbers are recorded.
The higher of the two numbers is the measure of the systolic pressure, which is the pressure on the blood vessels when the heart beats.
The systolic pressure of teenagers, in millimeters of Mercury (mmHg), is normally with mean μ and variance 32
The mean systolic pressure of a random sample of 40 teenagers is 105 mmHg
a) Conduct a 99% confidence Intervals for μ
b) it is claimed that teenagers have a mean systolic pressure of 104 mmHg

I really struggle with this so it be so helpful if someone could go through it
Last edited by going2fail; 2 months ago
0
2 months ago
#2
(Original post by going2fail)
When the blood pressure is measured two numbers are recorded.
The higher of the two numbers is the measure of the systolic pressure, which is the pressure on the blood vessels when the heart beats.
The systolic pressure of teenagers, in millimeters of Mercury (mmHg), is normally with mean μ and variance 32
The mean systolic pressure of a random sample of 40 teenagers is 105 mmHg
a) Conduct a 99% confidence Intervals for μ
b) it is claimed that teenagers have a mean systolic pressure of 104 mmHg

I really struggle with this so it be so helpful if someone could go through it
What do you understand about the problem/solution?
Is this a publically available exam question - if so, can you provide a link?

https://saylordotorg.github.io/text_...on-of-a-p.html
is a reasonable overview, but it will be covered in your textbook.
0
#3
(Original post by mqb2766)
What do you understand about the problem/solution?
Is this a publically available exam question - if so, can you provide a link?

https://saylordotorg.github.io/text_...on-of-a-p.html
is a reasonable overview, but it will be covered in your textbook.
X + z ×(σ/Square route of n)

It think X = 105 mmHg
Z =2.576
σ= Square root of 32 ( because of variance)
n= 40

Which entered into the equation equal 102.70 to 107.30. But I'm not whether I have answered what the question asks me to answer
And then I'm not sure about question b

Here is the paper it is question 3 a and b. It is just bellow the scatter diagrams

https://filestore.aqa.org.uk/resourc...Q-AM-2021.DOCX
1
2 months ago
#4
(Original post by going2fail)
X + z ×(σ/Square route of n)

It think X = 105 mmHg
Z =2.576
σ= Square root of 32 ( because of variance)
n= 40

Which entered into the equation equal 102.70 to 107.30. But I'm not whether I have answered what the question asks me to answer
And then I'm not sure about question b

Here is the paper it is question 3 a and b. It is just bellow the scatter diagrams

Thanks, your numbers are right. To be confident in an exam, you should try and understand the role of the different parts of the formula.
* If the standard deviation of the original distribution is large, you'd expect you're mean estimate to vary more. This is indeed the case as the standard deviation of the mean estimate is sigma/sqrt(n)
* If you have more data, you'd expect the mean estimate to be better (vary less). This is indeed the case as the standard deviation of the mean estimate is divided by sqrt(n).
* On average, you'd expect your mean estimate to be equal to the true mean. So the confidence interval is centered on the mean estimate +/- z*sigma/sqrt(n).
* The confidence interval specifies the inteval in which you expect the true mean, to a 99% confidence in this case, to lie.

So for b) does the data support / refute the claimed mean of 104 at a 99% level?

Note, it really is worth having a read through the section of your textbook.
Last edited by mqb2766; 2 months ago
2
#5
(Original post by mqb2766)
Thanks, your numbers are right. To be confident in an exam, you should try and understand the role of the different parts of the formula.
* If the standard deviation of the original distribution is large, you'd expect you're mean estimate to vary more. This is indeed the case as the standard deviation of the mean estimate is sigma/sqrt(n)
* If you have more data, you'd expect the mean estimate to be better (vary less). This is indeed the case as the standard deviation of the mean estimate is divided by sqrt(n).
* On average, you'd expect your mean estimate to be equal to the true mean. So the confidence interval is centered on the mean estimate +/- z*sigma/sqrt(n).
* The confidence interval specifies the inteval in which you expect the true mean, to a 99% confidence in this case, to lie.

So for b) does the data support / refute the claimed mean of 104 at a 99% level?

Note, it really is worth having a read through the section of your textbook.
Thank you that was really helpful
1
2 months ago
#6
(Original post by going2fail)
When the blood pressure is measured two numbers are recorded.
The higher of the two numbers is the measure of the systolic pressure, which is the pressure on the blood vessels when the heart beats.
The systolic pressure of teenagers, in millimeters of Mercury (mmHg), is normally with mean μ and variance 32
The mean systolic pressure of a random sample of 40 teenagers is 105 mmHg
a) Conduct a 99% confidence Intervals for μ
b) it is claimed that teenagers have a mean systolic pressure of 104 mmHg

I really struggle with this so it be so helpful if someone could go through it
i also had this question for the paper it confused me so much, the only question i found easy in this was the very last one about men and women heart rate.
0
2 months ago
#7
w

(Original post by going2fail)
X + z ×(σ/Square route of n)

It think X = 105 mmHg
Z =2.576
σ= Square root of 32 ( because of variance)
n= 40

Which entered into the equation equal 102.70 to 107.30. But I'm not whether I have answered what the question asks me to answer
And then I'm not sure about question b

Here is the paper it is question 3 a and b. It is just bellow the scatter diagrams

https://filestore.aqa.org.uk/resourc...Q-AM-2021.DOCX
welp i was far off from that, i kept doing random things on the calculator
1
#8
(Original post by Tzuyucherry)
w

welp i was far off from that, i kept doing random things on the calculator
Do you think I'm right? What kind of questions did you get? I've got my core maths paper at 2pm today🥲
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