In Exercises 3 – 8, test the claim about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed

3.  Can SAT scores predict college performance?  Let x be a variable that represents SAT score of a computer science major, and let y be a variable that represents a student’s GPA upon graduation.  A random sample of n =15 computer science majors provided their SAT scores and GPAs: x 1232 1070 1086 1287 1130 1048 1121 1095 1135 1208 1333 1160 1186 1243 1261 y 3.52 2.91 2.4 3.47 3.47 2.37 2.4 2.24 3.02 3.32 3.59 2.54 3.19 3.71 3.58   The scatter diagram for the SAT score and GPA is given below:   (a)  Find the sample correlation coefficient r.  Truncate to two decimal places.  What does the value tell you about the data? (b)  Find the equation of the least squares line .  Truncate to four decimal places.  What does the slope mean? (c)  Find the value of the coefficient of determination .  Truncate to two decimal places.  What does this number mean? (d)  What is the predicted GPA if a computer science major got a…

Express the alternative hypothesis in symbolic form. A psychologist claims that the mean amount of time​ (in hours) that females spend in talk therapy is more than that of men. Assume that two samples are independent. Let the female talk therapy times be the first population and the male talk therapy times be the second population.

In this exercise involving paired differences, consider that it is reasonable to assume the populations being compared have approximately the same shape and that the distribution of paired differences is approximately symmetric. A sample of 10 men was used in a study to test the effects of a relaxant on the time required to fall asleep. Suppose data for 10 subjects showing the number of minutes required to fall asleep with and without the relaxant follow. Relaxant Subject No Yes 1 14 14 9 2 13 10 3 23 12 4. 6 10 5 9 8 16 8 5 7 00 8 10 8 11 7 9 13 11 10 8 6 Use a 0.05 level of significance to determine whether the relaxant reduces the median time required to fall asleep. State the null and alternative hypotheses. Ho: Median time without relaxant - Median time with relaxant ≤ 0 Ha : Median time without relaxant - Median time with relaxant > 0 O Ho: Median time without relaxant - Median time with relaxant H : Median time without relaxant O Ho: Median time without relaxant - = 0 Median…