To test the efficacy of a certain diet cat food. a random sample of individuals is asked to weigh their cat. feed the cat the diet food for a month and weigh their cat a second time The weight of the cat is recorded each time. The data (in pounds) were recorded as Subject: 1 \( \qquad \) \( -2 \) 3 4 Pre-diet weight: \( \begin{array}{lllllllll}155 & 117 & 14.8 & 132 & 104 & 131 & 9.6\end{array} \) Post-diet weight: \( 153 \quad 115 \quad 144133101 \quad 12997 \) A paired t test is conducted on the data, with the difference Pre-diet - Post-diet paired by subject and \( \mathrm{H}_{\mathrm{a}} \) uDIFF \( >0 \) Assume that the paired differences come from a normally distributed population. 0.036 The p -value for this paired t test is \( = \) 0.190 0.157

To determine the p-value for your paired t-test, you'll need to calculate the mean difference between the pre-diet and post-diet weights for all subjects, as well as the standard deviation of those differences. After obtaining the t statistic, which compares the mean difference to the standard error, you can then find the p-value corresponding to this statistic using a t-distribution table or software. The smaller the p-value, the stronger the evidence against the null hypothesis. In your case, when testing whether the diet is effective (i.e., hoping the cats weigh less after the diet), a significance level of 0.05 is often used. If your calculated p-value is lower than this level, it indicates that the diet has a significant effect on decreasing cat weight.