Stat 185 Quiz practice

Here are a couple problems for group work that should help you with the quiz on Friday.

1. Suppose we've got the following list of grades:

   69

   66.5

   65

   64.3

   96

   66.5

   85.5

   61.9

   88

   66.5

   Run the hypothesis test
   • \(H_0: \mu=65\) vs
   • \(H_A: \mu>65\)
   at the 95% level of confidence. Be sure to
   1. Find the standard error,
   2. Find the test-statistic,
   3. Find the \(p\) value, and
   4. State the conclusion.
2. Suppose that a survey of 1223 likely District 11 voters finds that \(\hat{p}_D=0.505\) of them plan to vote for Davis but only \(\hat{p}_C=0.47\) of them plan to vote for Cawthorn. Run the hypothesis test
   • \(H_0:p_C=p_D\) vs
   • \(H_A: p_C < p_D\)
   at the 95% level of confidence. Be sure to
   1. Find the standard error,
   2. Find the test-statistic,
   3. Find the \(p\) value, and
   4. State the conclusion.
   Recall that, since this test involves multinomila proportions resulting from an election, you'll need to use the formula \[SE=\sqrt{\frac{(p_1+p_2)-(p_1-p_2)^2}{n}}.\]