1. A city health department wishes to determine if the mean bacteria count per unit volume of water at a lake beach is within the safety level of 200. A researcher collected 10 water samples of unit volume. The sample mean and sample variance for the bacteria counts are 191 and 121, respectively. Answer the following questions (using hand calculation) (10 points for each sub-question)
   1. Formulate the null and alternative hypotheses (Define any symbols you use).
   2. Determine the test statistic.
   3. Give the form of the rejection region.
   4. Calculate the p-value and make your conclusion at 0.05 significance level.
   5. Based on the results of d), what error could you have possibly made?