Question

Concerns about climate change and CO₂ reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 48 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.

(a) If the true mean is .9200 with a standard deviation of 0.0050, within what interval will 99 percent of the sample means fall? (Round your answers to 4 decimal places.)
  
The interval is from ? to ?

Answer 1

Solution :

Given that,

= 0.9200

= 0.0050

n = 48

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( /n)

=2.576 * (0.0050 / 48)

= 0.0019

At 99% confidence interval estimate of the population mean is,

- E < < + E

0.9200 - 0.0019 < <0.9200 + 0.0019

0.9181< < 0.9219

(0.9181, 0.9219)