Answer:
B. [3.86, 4.64]
Step-by-step explanation:
To find the 95% confidence interval for the average number of strokes, we need to have these following informations:
Sample size
Average of the sample
Standard deviation of the sample
Is this problem, we have that
Sample size = 64
Average = 4.25
Standard deviation = 1.6
Now, we need to find the degree of freedom and the value of , so we can find the a value that is needed for this calculus in the t-distribution table
The degree of freedom is the sample size subtracted by 1. So:
is the result of the subtraction of 1 by the confidence interval(decimal) divided by two. So
Looking at the t-distribution table, with , we find that the value is 1.998.
Now we need to multiply this value by the standard deviation of the sample and divide by the square root of the sample size. So:
Now
For the lower range of the interval, we subtract A from the mean
For the upper end of the interval, we add A to the mean
So
So the correct answer is
B. [3.86, 4.64]