Stat 185 Problem Sheet

Here are a couple problems for group work that should help you do this week's MyOpenMath assignment. As before, you should solve this problems together and then your group should send me one set of solutions as a private message on the forum. Be sure to include everyone's name in the message.

1. You wish to test the following claim (\(H_a\)) at a significance level of \(alpha = 0.1\). For the context of this problem, \(\mu_d = \mu_2 - \mu_1\) where the first data set represents a pre-test and the second data set represents a post-test. \[\begin{align} H_0: \mu_d &= 0 \\ H_A: \mu_d &> 0. \end{align}\] You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for \(n=44\) subjects. The average difference (post - pre) is \(\bar{d}=4.4\) with a standard deviation of the differences of \(\sigma_d=26.7\).
   1. What is the test statistic for this sample?
   2. What is the p-value for this sample?
   3. What is the conclusion of your hypothesis test?

2. This problem has a table you need to process. I've set up a little Colab Notebook to help with that process.

   A researcher takes sample temperatures in Fahrenheit of 16 days from Portland (Group 1) and 20 days from New York City (Group 2). Test the claim that the mean temperature in Portland greater than the mean temperature in New York City. Use a significance level of $\alpha=0.01$. Assume the populations are approximately normally distributed with unequal variances. Here's your data:

   Portland	New York City
   90.3	45.1
   75.8	34.2
   83.8	27.9
   78.7	45.1
   96.7	72.9
   83.3	58.5
   67.3	104.2
   70.4	44.3
   94.5	68.8
   97.4	52.5
   81.5	75.1
   81.5	64.9
   63.6	76.3
   89.3	83.7
   99.3	86.3
   88.9	70.8
   	49.4
   	85.4
   	61
   	76.3

   1. Write down the hypothesis test.
   2. Compute the test statistic.
   3. Compute the \(p\)-value.
   4. What is the conclusion of the hypothesis test?