# Mean

5 patients have a mean diastolic blood level of 95 are recruited for a study one month long. After one month the observed mean decline in diastolic blood pressure in these five patients is 4.8 with a standard deviation on 9.

7.32 how many patients would be needed to have a 90% chance of detecting a signifigant diff using a one tailed test with a signifigance level of 5%

7.33 Suppose we conduct a study of the preceding hypotheses based on 20 subjects. What is the probability that we will be able to reject H(0) using a one sided test at the 5% level?

Active Placebo active-pla

mean +- sd

average redness score:-0.61+-0.7 -0.04+-0.68 -.57+.86

(visit 2-Visit1 score)

7.83 Suppose we wish to estimate the number of subjects needed in a main study so that there will be a 90% chance of finding a signifigance level of 0.05 and we expect the active eyes to have a mean redness score 0.5 less than the placebo. How many subjects are needed in the study?

#### Solution Preview

7.32 how many patients would be needed to have a 90% chance of detecting a significant diff using a one tailed test with a significance level of 5%

The sample size formula uses three key factors:

(1) the significance level, the level of acceptable risk the researcher is willing to accept that the true margin of error exceeds the acceptable margin of error; i.e., the probability that differences revealed by statistical analyses really do not exist; also known as Type I error.

The alpha level used in determining sample size in this survey is a=1-0.95 =0.05. In the formula, the alpha level is incorporated into the formula by utilizing the t-value for the alpha level selected (e.g., t-value for alpha level of .05 is 1.66 for sample sizes above 120).

(2) Acceptable Margin of Error: ...

#### Solution Summary

5 patients have a mean diastolic blood level of 95 are recruited for a study one month long. After one month the observed mean decline in diastolic blood pressure in these five patients is 4.8 with a standard deviation on 9.

7.32 how many patients would be needed to have a 90% chance of detecting a signifigant diff using a one tailed test with a signifigance level of 5%

7.33 Suppose we conduct a study of the preceding hypotheses based on 20 subjects. What is the probability that we will be able to reject H(0) using a one sided test at the 5% level?

Active Placebo active-pla

mean +- sd

average redness score:-0.61+-0.7 -0.04+-0.68 -.57+.86

(visit 2-Visit1 score)

7.83 Suppose we wish to estimate the number of subjects needed in a main study so that there will be a 90% chance of finding a signifigance level of 0.05 and we expect the active eyes to have a mean redness score 0.5 less than the placebo. How many subjects are needed in the study?