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.
Margin of error = 1.96 * √(pq/n)
p = 52/150
q = 1 - p
n = 150
Convert fractions to decimals. Substitute decimals into the above equation and solve for margin of error.
I hope this will help get you started.
To find the margin of error (E) that corresponds to a 95% confidence level, we can use the formula:
E = Critical value * Standard error
The critical value for a 95% confidence level is 1.96.
To find the standard error, we need to determine the sample proportion (p̂) first:
p̂ = number of successful trials / total number of trials
In this case, the number of successful trials is 52 out of 150 trials. So:
p̂ = 52 / 150 = 0.3467 (approx.)
Now, we can calculate the standard error using the formula:
Standard error = √(p̂ * (1 - p̂) / n)
where n is the total number of trials. In this case, n is 150.
Standard error = √(0.3467 * (1 - 0.3467) / 150) ≈ 0.045
Finally, we can calculate the margin of error:
E = 1.96 * 0.045 ≈ 0.0882
Therefore, the margin of error (E) that corresponds to a 95% confidence level is approximately 0.0882.