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

Answer 1

The 99% confidence interval for mean is (0.9551, 0.9569).

Explanation:

The (1 - α)% confidence interval for the population mean is:

`CI=\bar x\pm z_(\alpha/2)\ (\sigma)/(√(n))`

The information provided is:

`n=33\\\bar x=\mu=0.956\\\sigma=0.002\\(1-\alpha) \%=99\%`

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample (
`\bar x`) approaches the whole population mean (µ).

In this case the sample size is quite large, i.e. n = 33 > 30. So, according to the law of large numbers, the sample mean is approximately same as the population mean.

The critical value of z for 99% confidence level is:

`z_(\alpha/2)=z_(0.005)=2.58`

*Use a z-table.

Compute the 99% confidence interval for mean as follows:

`CI=\bar x\pm z_(\alpha/2)\ (\sigma)/(√(n))`

`=0.956\pm 2.58* (0.002)/(√(33))\\=0.956\pm 0.0009\\=(0.9551, 0.9569)`

Thus, the 99% confidence interval for mean is (0.9551, 0.9569).