1 z-scores

  1. Use the transportation data to create a “percent” version of key variables (for example, percent of the population that bikes to work, etc).
  2. Now convert each of these into z-scores
  3. Calculate the mean and the standard deviation of these z-scores
  4. Calculate percentiles and quartiles
  5. Practice Problem 7.5

  1. What is the mpg (miles per gallon) that separates the (i) top 10% from the rest and (ii) the bottom 20%? You can use this applet or this applet.

2 Sampling

  1. Calculate the mean and median and standard deviation of the biking and walking and work at home variables, respectively.

  2. Draw a 1% sample of the counties from the transportation data and recalculate the statistics you calculated above.

  3. Now draw a 5% sample and repeat the preceding calculations.

  4. Now draw a 10% sample and repeat the preceding calculations.

3 The Binomial distribution

You can use this applet

  1. Problem 8.7

  1. Problem 8.11 (see the slide)

4 One-sample t-test

  1. Most people think that some 3% of workers commute to work by bicycle. Setup the null and alternative hypotheses and test this belief with \(\alpha = 0.05\). State your conclusion, as well as the corresponding confidence interval.

  2. Repeat the preceding test with \(\alpha = 0.01\) and state your conclusion, as well as the corresponding confidence interval.

  3. People also believe that some 5% walk to work every day. Test this belief, state your conclusion, and the corresponding confidence interval.

5 The Binomial test

  1. Test whether at least one-half of the population declares itself as a vegetarian. State your conclusion.

  2. Test whether at least one-third of the population believes in life after death. State your conclusion.