Concerns about climate change and CO2 reduction have initiat

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 36 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is 0.956 with a standard deviation of 0.005, within what interval will 95 percent of the sample means fall? (Round your answers to 4 decimal places.) The interval is from to

Solution

mean = 0.956

standard deviation = 0.005

z-score at 95% = 1.96

n= size of sample = 36

step1:
calculate standard error of mean

standard error of mean = z-score * standard deviation/sqrt(n)

= 1.96 * 0.005/sqrt(36)

= 0.0016

step 2:

upper limit = mean + standard error

= 0.956 + 0.0016

= 0.9576

lower limit = mean - standard error

= 0.956 - 0.0016

= 0.9544

hence

the interval is from 0.9544 to 0.9576