4) For the following sample data set, calculate the mean, variance, and standard deviation: 181 186 178 172 188 165 146 186 174 190 144 183 173 169 170 5) If the stated research (alternate) hypothesis is that there is a difference between the data sets from Question 3 and Question 4, the corresponding null hypothesis is that there is no difference between the data sets from Question 3 and Question 4. Compare the data sets from questions 3 and 4 using a non-directional (two-tailed) t test for independent means. From your calculations what are the degrees of freedom, t-statistic, and corresponding p-value? Provide a p-value plot (from StatCrunch options), as well as Summary Statistics (n, mean, standard deviation). 6. Using the data from questions 3 and 4 (displayed below), consider the following problem set- up. A physiologist wants to evaluate whether or not a treatment causes an observed measurement to significantly increase. Using a paired t test, the physiologist observes a measurement from 15 participants, administers a treatment, and then takes another measurement to see the impact of the treatment. The research hypothesis is that participants who receive the treatment have an increase in the second observation. The null hypothesis is that there is no difference between the first and second observation. Observation 1 (pre-treatment) Observation 2 (post-treatment) 158 181 191 186 132 178 184 172 166 188 142 165 185 146 196 186 174 174 188 190 185 144 174 183