1) A group of scientists created 150 trials to measure whether electric shock treatment could cure paranoid delusions. Of these trials, 52 were successful. Find the margin of error E that corresponds to a 95% confidence level. The critical value for 95% confidence level is 1.96

To find the margin of error (E) for a 95% confidence level, you first need to calculate the standard error (SE) using the following formula:

SE = sqrt(p * (1 - p) / n)

Where:
- p is the proportion of successful trials (52/150 = 0.347)
- n is the total number of trials (150)

SE = sqrt(0.347 * (1 - 0.347) / 150)
SE ≈ 0.041

Now, the margin of error (E) can be calculated by multiplying the standard error (SE) by the critical value for a 95% confidence level (1.96):

E = 1.96 * SE
E ≈ 1.96 * 0.041
E ≈ 0.080

Therefore, the margin of error E that corresponds to a 95% confidence level is approximately 0.080.