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 33 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.

(a) If the true mean is .9560 with a standard deviation of 0.0020, 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,

Point estimate = sample mean = = 0.9560

sample standard deviation = s = 0.0020

sample size = n = 33

Degrees of freedom = df = n - 1 = 33 - 1 = 32

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t0.005,32 = 2.738

Margin of error = E = t/2,df * (s /n)

= 2.738 * ( 0.0020 / 33)

Margin of error = E = 0.0010

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

  ± E  

= 0.9560 ± 0.0010

= ( 0.9550, 0.9570 )