Question

In a study of variation in systolic blood pressure upon application of leaches, it is found that the standard deviation of the 22 participants was 3.9 mmHg. It is understood that the standard deviation of blood pressure (in the absence of leeches) is 3.4 mmHg. We are interested in whether the standard deviation is different at the α=0.10 level of significance. What is the test statistic for this experiment?

Answer 1

Test statistic is [(n - 1) *S^2 ]/ σ ^2 = [(22 - 1) *(3.9)^2 ]/ (3.4) ^2

with 21 degrees of freedom

Yes this data fits at the 10% level of significance, so I would not reject that statistic of 3.9 mmHg as a wrong standard deviation

Explanation:

use the expression I attached in the image to find

[(n - 1) *S^2 ]/ σ ^2

where S = the standard deviation calculated from the sample of n trials.

sigma is the population standard deviation.

[(22 - 1) *(3.9)^2 ]/ (3.4) ^2 = 21 * 15.21 / 11.56 = 27.6306

all we have to do now is to make sure this number is in the 90 % confidence

interval. remember this has 21 degrees of freedom, look at the chi-squared chart.

11.5913 < 27.6306 < 32.67905

where 11.5913 is the lower bound of the chart

and 32.67905 is the upper bound