Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 40.9 for a sample of size 20 and standard deviation 11.7. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level). Assume the data is from a normally distributed population.

Enter your answer as a tri-linear inequality accurate to three decimal places

Answer 1

Answer:

Given that,

The effectiveness of a blood-pressure drug is being investigated.

An experimenter finds that, on average, the reduction in systolic blood pressure is 40.9 for a sample of size 20 and a standard deviation of 11.7.

i.e,

=40.9

n=20 And, =11.7

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level):

Given,

Assume the data is from a normally distributed population.

In order to obtain the lower patient's blood pressure. We first obtain the confidence interval and the lower value of the confidence interval indicates the patient's lower systolic blood pressure.

For this let us consider, the null and alternative hypothesis as follows:

Where and is the null and alternative hypothesis.

The confidence interval for the level of significance is given as,

Where,

The level of significance =1-98%=1-0.98=0.02

/2=0.01

The Z-critical value is obtained considering the normal distribution for a two-tailed confidence interval which is obtained for given level of significance.

i.e,

For a 98% confidence interval,

=(34.935, 46.865) (Approximately)

Therefore, the a 98% confidence interval is (34.935, 46.865).