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

(a) If the true mean is .9660 with a standard deviation of 0.0060, within what interval will 98 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 = = 0.9660

sample standard deviation = s = 0.0060

sample size = n = 46

Degrees of freedom = df = n - 1 = 46 - 1 = 45

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

t/2,df = t_0.01,45 = 2.412

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

= 2.412 * ( 0.0060 / 46)

Margin of error = E = 0.0021

The 98% confidence interval estimate of the population mean is,

  ± E

= 0.9660 ± 0.0021

= ( 0.9639  to 0.9681 )