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- Psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded. Hours without sleep 32 38 48 24 46 35 30 34 42 Number of Mistakes 6 8 13 5 7 6 5 8 12 Hours without sleep=x, Number of mistakes=y (a) When you test the claim at the α = 0.01, that a linear relation exists between the two variables, find the critical value. Round critical value to nearest hundredth. (e.g. 0.135 would be entered as 0.14, -0.135 would be entered as -0.14, ± 0.135 would be entered as +/-0.14). (b) Find 95% confidence interval about the slope of the true lease-square regression line. Lower , Upper . Round confidence interval to nearest thousandth. e.g. 2.3457 would be entered as 2.346 (c) Based on question (b), does any linear relation exist between hours without sleep and number of mistakes? . (Enter yes or no,…Which of the following statements is the most correct statement regarding the critical points of the following function: y = ax3 + bx² + cx+d a. There are no critical points b. There will be a minimum of two critical points c. There will be a maximum of two critical points d. There can be any number of critical pointsDetermine all critical points of the given function if there are any. Make sure to determine the domain. Show the complete solution. 1. ?(?)=?√4−?2 2. ?(?)=4/(?−1)2
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