e. Which of the following is an appropriate conclusion?- ○ Given that $ p < \alpha $ at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the tutor is, in fact, effective.- ○ Given that $ p > \alpha $ at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the tutor is, in fact, effective.- ○ Given that $ p > \alpha $ at a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the tutor is, in fact, effective.- ○ Given that $ p < \alpha $ at a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the tutor is, in fact, effective. **Testing Paired Samples**A statistics tutor wishes to study the effect that his tutoring has on his students. He randomly selects 4 new students and records their current grades in their statistics courses. After half a semester of tutoring, the students' grades are recorded again. The statistics tutor then uses a paired, two-sample hypothesis test to determine if the differences between the before and after grades are statistically significant. (The tutor assumes a 5% level of significance.)| Students | A | B | C | D ||----------|----|----|----|----|| Before | 83 | 78 | 93 | 87 || After | 80 | 80 | 96 | 86 |**Useful tools:**- [Normal Distribution Calculator](#)- [t-Distribution Calculator](#)**Questions:**a. Which of the following null and alternative hypotheses match this scenario?- [ ] $ H_0 : \Delta \mu \geq 0 $ $ H_a : \Delta \mu = 0 $ - [ ] $ H_0 : \Delta \mu \leq 0 $ $ H_a : \Delta \mu > 0 $ - [ ] $ H_0 : \Delta \mu > 0 $ $ H_a : \Delta \mu \leq 0 $b. Which type of test should be applied?- [ ] The alternative hypothesis indicates a right-tailed test.- [ ] The alternative hypothesis indicates a left-tailed test.- [ ] The alternative hypothesis indicates a two-tailed test.c. Which type of distribution should be applied?- [ ] The required distribution is a Normal Distribution.- [ ] The required distribution is Student's t-Distribution.- [ ] The required distribution is a Binomial Distribution approximated by a Normal Distribution.d. Calculate the p-value from this hypothesis test.$ p = $

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Answered: Testing Paired Samples A statistics…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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