1. You are interested in the performance of an image compression algorithm.
   Let us say that, for a corpus of images, the mean compression time is
   80ms with standard deviation 20ms. 
   Note: In each case make and state any necessary assumptions.

   a) Consider random samples of size 64 images that could be selected from 
      this corpus. Given the sampling distribution of ybar, what proportion of 
      samples would you expect to result in ybar greater than 91ms.
   b) Consider samples of size 17 images instead of samples of size 64
      images. Given this sample size, do you think your answer to a) would
      be different? Justify your answer.


2. A usability analyst is interested in evaluating a browser-based interface.
   She decides to conduct a controlled experiment and selects a sample of 
   36 users for observation. She provides them with a suite of tasks
   and observes the number of errors made in completing the task suite. She
   discovers that the mean error count is 15 with standard deviation of 8.
   Note: In each case make and state any necessary assumptions.

   a) Provide a point estimate for the mean error count of the population.
   b) Determine the error in your estimate of the population mean.
   c) Determine the margin of error for your estimate of the population mean.
   d) Construct and interpret an 80% confidence interval for the population 
      mean. 
   e) i) Construct and interpret a 99% confidence interval for the population 
         mean. 
     ii) Let us say your sample consisted of 26 users instead of 36 users.
         Construct and interpret a 99% confidence interval for the population 
         mean given this new sample size.