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Stats, A-level Maths - Help with confidence intervals

Could someone briefly explain confidence intervals and in the formula below, How do you work out z?

Confidence Interval = μ ± z (σ/√n).

E.g. If n = 50, Σx = 286.5 and Σ(x-x̄)² = 45.16
s.d. = 0.96
μ = 5.73
How would you construct a 99% interval?
Reply 1
Avatar for Mav455
Mav455
17
For confidence intervals the formula is basically:
TO FIND THE UPPER LIMIT = the mean (5.73) + Z-Value(2.5758) X SD/Square root of N (0.96 divided by square root of 50) ANS=6.08
TO FIND THE LOWER LIMIT = the mean (5.73) - Z-Value(2.5758) X SD/Square root of N(0.96 divided by square root of 50) ANS=5.38
The Confidence Interval is therefore 5.38 to 6.08
To find the Z-Value, take whatever percentage you have and identify how much you need to add to make it 100, So in the case of 99%, you need to add 0.01 (as 0.99 + 0.01 = 1). After identifying this, you then HALF the number, so half of 0.01 is 0.005 and then add this to the C,I, (0.99). 0.99 + 0.005 = 0.995. This is the value you look up in Table 4 of the AQA formula booklet. For 0.995, the Z-Value is 2.5758

Hope that helped, quote me if you need any more help :smile:
Reply 2
Avatar for Mav455
Mav455
17
For confidence intervals the formula is basically:
TO FIND THE UPPER LIMIT = the mean (5.73) + Z-Value(2.5758) X SD/Square root of N (0.96 divided by square root of 50) ANS=6.08
TO FIND THE LOWER LIMIT = the mean (5.73) - Z-Value(2.5758) X SD/Square root of N(0.96 divided by square root of 50) ANS=5.38
The Confidence Interval is therefore 5.38 to 6.08
To find the Z-Value, take whatever percentage you have and identify how much you need to add to make it 100, So in the case of 99%, you need to add 0.01 (as 0.99 + 0.01 = 1). After identifying this, you then HALF the number, so half of 0.01 is 0.005 and then add this to the C,I, (0.99). 0.99 + 0.005 = 0.995. This is the value you look up in Table 4 of the AQA formula booklet. For 0.995, the Z-Value is 2.5758

Hope that helped, quote me if you need any more help :smile:
Reply 3
Avatar for Pumuki63
Pumuki63
OP
10
Original post by Mav455
For confidence intervals the formula is basically:
TO FIND THE UPPER LIMIT = the mean (5.73) + Z-Value(2.5758) X SD/Square root of N (0.96 divided by square root of 50) ANS=6.08
TO FIND THE LOWER LIMIT = the mean (5.73) - Z-Value(2.5758) X SD/Square root of N(0.96 divided by square root of 50) ANS=5.38
The Confidence Interval is therefore 5.38 to 6.08
To find the Z-Value, take whatever percentage you have and identify how much you need to add to make it 100, So in the case of 99%, you need to add 0.01 (as 0.99 + 0.01 = 1). After identifying this, you then HALF the number, so half of 0.01 is 0.005 and then add this to the C,I, (0.99). 0.99 + 0.005 = 0.995. This is the value you look up in Table 4 of the AQA formula booklet. For 0.995, the Z-Value is 2.5758

Hope that helped, quote me if you need any more help :smile:


Thank you very much!! That makes a lot more sense!! :biggrin:

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