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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 D Before 83 78 93 87 After 80 80 96 86 Useful tools: Normal Distribution Calculator t-Distribution Calculator a. Which of the following null and alternative hypotheses match this scenario? Ho:Aµ 2 0 H4: Δμ- 0 Ο H0: Δμ <0 Η: Δμ > 0 O Ho:Aµ > 0 Η: Δμ <0 b. Which type of test should be applied? The alternative hypothesis indicates a right-tailed test. O The alternative hypothesis indicates a left-tailed test. O The alternative hypothesis indicates a two-tailed test. c. Which type of distribution should be applied? O The required distribution is a Normal Distribution. O The required distribution is Student's t-Distribution. The required distribution is a Binomial Distribution approximated by a Normal Distribution.

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 D Before 83 78 93 87 After 80 80 96 86 Useful tools: Normal Distribution Calculator t-Distribution Calculator a. Which of the following null and alternative hypotheses match this scenario? Ho:Aµ 2 0 H4: Δμ- 0 Ο H0: Δμ <0 Η: Δμ > 0 O Ho:Aµ > 0 Η: Δμ <0 b. Which type of test should be applied? The alternative hypothesis indicates a right-tailed test. O The alternative hypothesis indicates a left-tailed test. O The alternative hypothesis indicates a two-tailed test. c. Which type of distribution should be applied? O The required distribution is a Normal Distribution. O The required distribution is Student's t-Distribution. The required distribution is a Binomial Distribution approximated by a Normal Distribution.

MATLAB: An Introduction with Applications
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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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.
Transcribed Image Text: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. \( p = \)
Transcribed Image Text:**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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