Question

The developmental department for a National Lawn Care Services Provider is interested in improving products and services. The germination periods, in days, for grass seed are normally distributed with a population standard deviation of 7 days and an unknown population mean. If a random sample of 17 types of grass seed is taken and results in a sample mean of 37 days, find the error bound (EBM) of the confidence interval with a 98% confidence level.

Answer 1

3.949

Explanation:

We can use the formula to find the error bound:

EBM=(zα/2)(σn/√)

We know that σ=7 and n=17. We are also given that the confidence level (CL) is 98%, or 0.98. So, we can calculate alpha (α).

α=1−CL

=1−0.98

=0.02

Since α=0.02, we know that

α2=0.022=0.01

The value of z0.01 is 2.326. Now we can substitute the values into the formula to find the error bound.

EBM=(zα/2)(σ/√n)

=(2.326)(7/√17)

≈(2.326)(1.698)

≈3.949

So, the error bound (EBM) is 3.949.