(Use Excel for all your work)
1. The observations in the Excel data file SHEET 1 are the ages of a random sample of 8 men in a bar. It is known that the ages are normally distributed with a standard deviation of 10. Determine the 95% confidence interval estimate of the mean.
2. It is known that the amount of time needed to change the oil in a car is normally distributed with a standard deviation of 5 minutes. The amount of time to complete a random sample of 10 oil changes was recorded and listed in the Excel data file SHEET 2. Compute the 99% confidence interval estimate of the mean of the population.
Step 1: Use AVERAGE function to find the sample mean from the data.
Step 2: Use the function CONFIDENCE.NORM (Formulas -> More functions -> Statistical) to combine the mean and the population standard deviation (given in the problem) along with the given value of α using the formulation:
Sample mean ± CONFIDENCE.NORM(alpha, std. dev., sample size)
Use normdist function: normdist(x,mean, std.dev, cumulative), where cumulative = TRUE if computing P(X < k) and cumulative = FALSE if computing P(X = k). See the practice problems from Chapter 8 for more info, if desired.
Clearly state the functions you are using along with the input arguments (if clicking on the answer displays the function at the top, that’s ok too).