45 In an effort to improve the mathematical skills of 12 students, a teacher provides a weekly 1-hour tutoring session. A pre-test is given before the sessions and a post-test is given after. The results are shown here. Test the claim that there was an increase in the scores at $\alpha=0.01$. You believe that the population is normally distributed, but you do not know the standard deviation. When calculating the difference, use Post-test minus Pre-test.| Pre-test | Post-test ||----------|-----------|| 86 | 86 || 60 | 58 || 88 | 81 || 82 | 75 || 50 | 49 || 58 | 54 || 67 | 64 || 78 | 80 || 49 | 42 || 57 | 55 || 51 | 49 || 92 | 100 |**Which of the following are the correct hypotheses?**- $ H_0 : \mu_d \geq 0 $- $ H_A : \mu_d < 0 $ (claim)- $ H_0 : \mu_d \leq 0 $- $ H_A : \mu_d > 0 $ (claim)- $ H_0 : \mu_d = 0 $- $ H_A : \mu_d \neq 0 $ (claim)Given that $\alpha = 0.01$, the critical value is 2.718.- The test statistic is: _____ (round to 3 places)- The p-value is: _____ (round to 3 places)The decision can be made to:- ○ reject $ H_0 $- ○ do not reject $ H_0 $The final conclusion is that:- ○ There is enough evidence to reject the claim that there was an increase in the scores.- ○ There is not enough evidence to reject the claim that there was an increase in the scores.- ○ There is enough evidence to support the claim that there was an increase in the scores.- ○ There is not enough evidence to support the claim that there was an increase in the scores.

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved. a) To testH0:μd≤0HA:μd>0 b) x y d=x-y d-d (d-d)2 86 86 0 -2.08333 4.340276 60 58 2 -0.08333 0.006944 88 81 7 4.916667 24.17361 82 75 7 4.916667 24.17361 50 49 1 -1.08333 1.17361 58 54 4 1.916667 3.673612 67 64 3 0.916667 0.840278 78 80 -2 -4.08333 16.67361 49 42 7 4.916667 24.17361 57 55 2 -0.08333 0.006944 51 49 2 -0.08333 0.006944 92 100 -8 -10.0833 101.6736 Total 25 200.9167 whered=∑dn=2512=2.083333 Andsd=∑d-d2n-1=200.916712-1=200.916711=18.2651=4.274 Then, the test statistic ist=dsd/n=2.0833334.274/12=2.0833331.2338=1.688c) The degree of freedom=n-1=12-1=11 Then, the p-value in the one tail is .060.

Math

Probability

In an effort to improve the mathematical skills of 12 students, a teacher provides a weekly 1-hour tutoring session. A pre-test is given before the sessions and a post-test is given after. The results are shown here. Test the claim that there was an increase in the scores. at æ=0.01. You believe that the population is normally distributed, but you do not know the standard deviation. When calculating difference use Post- test minus Pre-test. pre-test post-test 86 86 60 58 88 81 82 75 50 49 58 54 67 64 78 80 49 42 57 55 51 49 92 100 Which of the following are the correct hypotheses? O Ho: Ha 2 0 HA: Hd < 0(claim) Но: ра < 0 HA: Hd > 0(claim) O Ho: Hd HA: Ha + 0(claim) Given that a is 0.01 the critical value is 2.718 The test statistic is: (round to 3 places) The p-value is: (round to 3 places)

In an effort to improve the mathematical skills of 12 students, a teacher provides a weekly 1-hour tutoring session. A pre-test is given before the sessions and a post-test is given after. The results are shown here. Test the claim that there was an increase in the scores. at æ=0.01. You believe that the population is normally distributed, but you do not know the standard deviation. When calculating difference use Post- test minus Pre-test. pre-test post-test 86 86 60 58 88 81 82 75 50 49 58 54 67 64 78 80 49 42 57 55 51 49 92 100 Which of the following are the correct hypotheses? O Ho: Ha 2 0 HA: Hd < 0(claim) Но: ра < 0 HA: Hd > 0(claim) O Ho: Hd HA: Ha + 0(claim) Given that a is 0.01 the critical value is 2.718 The test statistic is: (round to 3 places) The p-value is: (round to 3 places)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

In an effort to improve the mathematical skills of 12 students, a teacher provides a weekly 1-hour tutoring session. A pre-test is given before the sessions and a post-test is given after. The results are shown here. Test the claim that there was an increase in the scores at $\alpha=0.01$. You believe that the population is normally distributed, but you do not know the standard deviation. When calculating the difference, use Post-test minus Pre-test.

| Pre-test | Post-test |
|----------|-----------|
| 86 | 86 |
| 60 | 58 |
| 88 | 81 |
| 82 | 75 |
| 50 | 49 |
| 58 | 54 |
| 67 | 64 |
| 78 | 80 |
| 49 | 42 |
| 57 | 55 |
| 51 | 49 |
| 92 | 100 |

**Which of the following are the correct hypotheses?**

- $ H_0 : \mu_d \geq 0 $
- $ H_A : \mu_d < 0 $ (claim)

- $ H_0 : \mu_d \leq 0 $
- $ H_A : \mu_d > 0 $ (claim)

- $ H_0 : \mu_d = 0 $
- $ H_A : \mu_d \neq 0 $ (claim)

Given that $\alpha = 0.01$, the critical value is 2.718.

- The test statistic is: _____ (round to 3 places)

- The p-value is: _____ (round to 3 places)

The decision can be made to:

- ○ reject $ H_0 $
- ○ do not reject $ H_0 $

The final conclusion is that:

- ○ There is enough evidence to reject the claim that there was an increase in the scores.
- ○ There is not enough evidence to reject the claim that there was an increase in the scores.
- ○ There is enough evidence to support the claim that there was an increase in the scores.
- ○ There is not enough evidence to support the claim that there was an increase in the scores.

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