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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
- [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.
\( p = \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedd99afd-48e9-4e8a-b434-1d3cd4c035a5%2F08ff00c1-948e-4454-98f2-47fd54c40167%2Fj18hbu7_processed.png&w=3840&q=75)
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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