A 48-year old man is referred for evaluation of possible hypertension. On the basis of ten measurements, the patient's average diastolic blood pressure is 113mmHg, and the standard deviation is 8mmHg. If four rather than ten measurements of the mean blood pressure are made, which of the following is the expected impact on the size of the 95% confidence interval about the mean blood pressure?
A) Change, but the direction cannot be predicted
B) Decrease in width
C) Increase in width
D) Remain the same
As far as I know, and allegedly, the answer is C.
But I chose A because you never know what would happen to 4 newly measured values' standard deviation. I mean, it was 8mmHg when you measured 10 times, there is possibility it would be 1mmHg when measured 4 times with minor probability. I also understand that you should use σ(the population standard deviation), but you can use s(standard deviation within sample) instead where you can't find σ, which happens almost always in the field of inferential statistics including this situation.
So if this is the case, the size of the 95% confidence interval decrease even if (root 10) is larger than (root 4), because 8mmHg is far larger than 1mmHg.
And of course there is possibility that 95% confidence interval remains same contrary to choice A, but the chance is nearly zero because blood pressure is interval scale. If you take any 2 real number which is interval scale between 0 and 1 , the chance that you get same 2 number is zero.
These were the reasons why I thought A is answer.
Please tell me what's the right way to think.
A) Change, but the direction cannot be predicted
B) Decrease in width
C) Increase in width
D) Remain the same
As far as I know, and allegedly, the answer is C.
But I chose A because you never know what would happen to 4 newly measured values' standard deviation. I mean, it was 8mmHg when you measured 10 times, there is possibility it would be 1mmHg when measured 4 times with minor probability. I also understand that you should use σ(the population standard deviation), but you can use s(standard deviation within sample) instead where you can't find σ, which happens almost always in the field of inferential statistics including this situation.
So if this is the case, the size of the 95% confidence interval decrease even if (root 10) is larger than (root 4), because 8mmHg is far larger than 1mmHg.
And of course there is possibility that 95% confidence interval remains same contrary to choice A, but the chance is nearly zero because blood pressure is interval scale. If you take any 2 real number which is interval scale between 0 and 1 , the chance that you get same 2 number is zero.
These were the reasons why I thought A is answer.