1. Many types of error will cause a computer program to terminate or give incorrect results. One type of error is punctuation. For instance, if a comma is inserted in the wrong place, the program might not run. A study of programs written by students in an introductory programming course showed that 75 out of 300 errors selected at random were punctuation errors. Round your answers to THREE decimal places. the article, (a) Find 99% confidence interval for the proportion of errors made by beginning programming students that are punctuation errors. Interpret the results in a clear sentence (hint, for correct wording, see Section 7.1 notes). (8 pt) Margin of Error: 99% Confidence Interval: Interpretation Statement: (b) Find a 95% confidence interval. Is this interval longer or shorter? Why? (8 pt) Margin of Error: 95% Confidence Interval: Longer or Shorter and Why? (Hint: similar question in an example in 7.1 Notes) 2. The manager for a radio station wants to estimate the mean length of all songs published after 1960. How many songs should be in the sample if we want 90% confidence that the sample mean is within 15 seconds 2.625 minutes. (Hints: Watch the units here (they need to be of the population mean? Assume that = consistent) and remember the rounding rules for sample sizes). (5) Sample size required: