Suppose blood pressure values follow a normal distribution. Below are the blood

Question

Suppose blood pressure values follow a normal distribution. Below are the blood pressure values (in mmHg) for 9 randomly selected individuals: 118.6, 127.4, 138.4, 130.1, 113.7, 122.0, 108.3, 131.5, 133.2. Calculate the sample mean and sample variance. (You must show your calculation steps to earn credits. Any answer with no work will receive zero credit.) Calculate a 99% confidence interval for the population mean blood pressure. (You must show your calculation steps to earn credits Any answer with no work will receive zero credit.) Interpret the confidence interval calculated above. Calculate a 90% prediction interval for a future sample blood pressure value. (You must show your calculation steps to earn credits. Any answer with no work will receive zero credit.) Interpret the prediction interval calculated above.

Explanation / Answer

1) from above

hence mean =124.8

and std deviation=(777/8)1/2 =9.855

2) for std error =std deviation/(n)1/2 =3.285

and for 8 degree of freedom and 99% CI, t=3.3554

hence confidence interval =sample mean -/+ t*std error =113.7773 ; 135.8227

3) this confidence interval gives 95% probability to contain true mean of population

4)std error for prediction =std deviation(1+1/n)1/2 =10.388

hence prediction interval =sample mean -/+ t*std error =89.9432 ; 159.6568

5) this interval gives 95% probability to predict true mean of population

X (X-mean)^2 118.6 38.44 127.4 6.76 138.4 184.96 130.1 28.09 113.7 123.21 122 7.84 108.3 272.25 131.5 44.89 133.2 70.56 total 1123.2 777 mean=total/9 124.8

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