Question

Many companies marketing department use confidence intervals when estimating their future sales. A business decision that would or should be made using confidence intervals is a t-shirt company . They sells only all plain white T-shirts. The t-shirt company knows that they will sell more large t-shirts, than any other T-shirt sizes. How do they know how to many size large , x-large , xx large , or xxx large shirts to stock. What data do they need to do a confidential interval. The company plans has 10,000 customers and will use a 100 customers sample. The sample mean for the number of large shirts is 41. The standard deviation is 7. Using a 95% confidence interval.

What is the confidence interval for large white t-shirts?

Answer 1

sample mean, xbar = 41
sample standard deviation, s = 7
sample size, n = 100
degrees of freedom, df = n - 1 = 99

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.984

CI = (41 - 1.984 * 7/sqrt(100) , 41 + 1.984 * 7/sqrt(100))
CI = (39.6112 , 42.3888)

X - te X X te x Vn CI n