Question

In a sample of 18 small candles, the weight is found to be 3.72 ounces with a standard deviation of 0.963 ounces. What would be the 87% confidence interval for the size of the candles, assuming the data are normally distributed?

Answer 1

It is given that

x(bar) = sample mean = 3.72

sample size n = 18

sample standard deviation s = 0.963

it is clear that the population variance is unknown and sample size is less than 30, so we will use t distribution for the calculation of confidence interval

Using the confidence interval formula

we need to find the value of t for 87% confidence interval

degree of freedom = n-1 =18-1 = 17

Using the t distribution table for 87% confidence level and df = 17, we get t critical = 1.591

(check for df in left most column and check alpha level 1-0.87 = 0.13 in the top most row, then selecting intersecting cell)

setting all the given values, we get

this gives us

Therefore, required 87% confidence interval is (3.359, 4.081)

(Answer is rounded to 3 decimals)