A random sample of 15 subjects was asked to perform a given task. The time in seconds it took each of them to complete the task is recorded below.37, 33, 28, 29, 37, 50, 28, 45, 49, 30, 39, 27, 40, 48, 26Send data to calculatorIf we assume that the completion times are normally distributed, find a 95% confidence interval for the true mean completion time for this task. Give the lower limit and upper limit of the 95% confidence interval.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit: Upper limit:
Question
A random sample of 15 subjects was asked to perform a given task. The time in seconds it took each of them to complete the task is recorded below.37, 33, 28, 29, 37, 50, 28, 45, 49, 30, 39, 27, 40, 48, 26Send data to calculatorIf we assume that the completion times are normally distributed, find a 95% confidence interval for the true mean completion time for this task. Give the lower limit and upper limit of the 95% confidence interval.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit: Upper limit:
Solution
To find the 95% confidence interval for the true mean completion time, we first need to calculate the sample mean (x̄) and the standard deviation (s).
Step 1: Calculate the sample mean (x̄) Add up all the times and divide by the number of subjects (15). x̄ = (37+33+28+29+37+50+28+45+49+30+39+27+40+48+26) / 15 = 37.6
Step 2: Calculate the standard deviation (s) First, find the variance. Subtract the mean from each time, square the result, add all these, and divide by the number of subjects minus 1. Then, take the square root of the variance to get the standard deviation. Variance = [(37-37.6)^2 + (33-37.6)^2 + ... + (26-37.6)^2] / (15-1) Standard deviation (s) = sqrt(Variance)
Step 3: Find the standard error (SE) SE = s / sqrt(n), where n is the number of subjects (15).
Step 4: Find the 95% confidence interval The 95% confidence interval is x̄ ± (t*SE), where t is the t-score. For a 95% confidence interval and degrees of freedom (n-1 = 14), the t-score is approximately 2.145.
Lower limit = x̄ - (tSE) Upper limit = x̄ + (tSE)
Round your answers to one decimal place.
Note: The standard deviation and standard error calculations require a calculator with statistical functions or a statistical software.
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