Question

The WHO says that humans caused approximately 1.0° F of global warming above preindustrial levels (on average). The 66% confidence interval is 0.9° F to 1.3° F. If the WHO relied on a sample of 100 temperatures over several 19 years to find the sample average of 1.0°C (x bar), and that the standard deviation of the population of temperatures over the 19 years is known (sigma), what is the approximate distribution of X bar? What is the standard normal critical value used to create a 66% confidence interval centered at zero? i.e. Solve for z, where P⁡(-z ≤ Z ≤ z) = 66%. (IMPORTANT: Find z to the closest hundredth; you must not interpolate to get a more precise answer.) Use the answers to (a) and (b) to solve for sigma. After finding sigma, find the 95% confidence interval for the population mean of temperatures over the 19 years.

Answer 1

z-value for 66% CI = 0.9542

mean - 0.9542*sigma/sqrt(100) = 0.9
mean + 0.9542*sigma/sqrt(100) = 1.3

solving the above two equations, we get
mean = (0.9 + 1.3)/2 = 1.1
xbar = 1.1

sigma = ((0.9 - 1.1)/0.9542)*10 = -2.0960