Question

In: Statistics and Probability

Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel...

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 ?

Solutions

Expert Solution

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 = Z0.005 = 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)


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