The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At a = 0.01, is there enough evidence to conclude that their scores improved the second time they took the test?StudentScore on first test9 10 11 12 13 14 e638 634 436 555 612 443 337 414 450 492 491 527 336 488Score on second test 643 652 456 567 570 461 304 429 459 520 529 566 373 5281|234 56Identify the claim and state Hg and Ha-The claim is "The students' critical reading test scoresthe second time they took the test."Let Ha be the hypothesized mean of the the students' first score minus their second score. State Ho and Hg. Choose the correct answer below.O A. Hg: Hd 0O B. Họ: He2dOC. Họ: H saHạ: He aOD. Hg: Hd S0O E. Ho: Hd * 0OF. Hg: He 20Ha: Ha =0Calculate d and Sd-(Type an integer or a decimal. Round to three decimal places as needed.)Calculate sg.(Type an integer or a decimal. Round to three decimal places as needed.)Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.O Fail to reject the null hypothesis.Reject the null hypothesis.Interpret the decision in the context of the original claim. Choose the correct answer below.O A. The sample was not large enough to make a conclusion.O B. At the 1% significance level, there is not enough evidence that the students' critical reading scores improved the second time they took the test.OC. At the 1% significance level, there is enough evidence that the students' critical reading scores improved the second time they took the test.O D. At the 1% significance level, there is evidence that the students' critical reading scores got worse the second time they took the test.

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Description: The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At a = 0.01, is there enough evidence to conclude that their scores improved the second time they took the test?StudentScore on firs

The claim of the test is 'The students critical reading test scores improved the second time they took the test'. Let μd be the mean difference of first score and second score, d=first score-second score. The hypotheses are, Null hypothesis: H0:μd≤0 Alternative hypothesis: Ha:μd<0 Correct Answer: Option F. The difference is, Score on first test Score on second test Difference 638 643 -5 634 652 -18 436 456 -20 555 567 -12 612 570 42 443 461 -18 337 304 33 414 429 -15 450 459 -9 492 520 -28 491 429 62 527 566 -39 336 373 -37 488 528 -40 ∑d=-104 The mean difference is, d¯=∑dn=-10414=-7.429 Thus, the mean difference is -7.429. The standard deviation difference is, sd=∑d-d¯2n-1=-5+7.4292+-18+7.4292+…+-40+7.429214-1=12721.4313=978.5714=31.282 Thus, the standard deviation difference is 31.282.The test statistic is, t=d¯-μdsdn=-7.429-031.28214=-7.4298.3605=-0.8886 The test statistic is -0.8886. The degrees of freedom is, df=n-1=14-1=13 The degrees of freedom is 13. The hypothesis is left tail. The probability of t less than –0.8886 with 13 degrees of freedom can be obtained using the excel formula “=T.DIST(–0.8886,13,TRUE)”.The p-value is 0.1952. Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.1952) is greater than the level of significance (0.01). Based on decision rule, fail to reject the null hypothesis. Thus, there is not enough evidence that the students' critical reading scores improved the second time they took the test. Correct Answer: Option B.

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Statistics

The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At a=0.01, is there enough evidence to conclude that their scores improved the second time they took the test? Student Score on first test 789 10 11 12 13 14e 638 634 436555 612 443 337414 450 492 491 527 336 488 Score on second test 643652 456 567 570 461 304 429459 520 529 566 373 528 123 4 5 6 Identify the claim and state Hg and Hg-

The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At a=0.01, is there enough evidence to conclude that their scores improved the second time they took the test? Student Score on first test 789 10 11 12 13 14e 638 634 436555 612 443 337414 450 492 491 527 336 488 Score on second test 643652 456 567 570 461 304 429459 520 529 566 373 528 123 4 5 6 Identify the claim and state Hg and Hg-

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At a = 0.01, is there enough evidence to conclude that their scores improved the second time they took the test?
Student
Score on first test
9 10 11 12 13 14 e
638 634 436 555 612 443 337 414 450 492 491 527 336 488
Score on second test 643 652 456 567 570 461 304 429 459 520 529 566 373 528
1|2
3
4 5
6
Identify the claim and state Hg and Ha-
The claim is "The students' critical reading test scores
the second time they took the test."
Let Ha be the hypothesized mean of the the students' first score minus their second score. State Ho and Hg. Choose the correct answer below.
O A. Hg: Hd 0
O B. Họ: He2d
OC. Họ: H sa
Hạ: He a
OD. Hg: Hd S0
O E. Ho: Hd * 0
OF. Hg: He 20
Ha: Ha =0
Calculate d and Sd-
(Type an integer or a decimal. Round to three decimal places as needed.)
Calculate sg.
(Type an integer or a decimal. Round to three decimal places as needed.)
Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.
O Fail to reject the null hypothesis.
Reject the null hypothesis.
Interpret the decision in the context of the original claim. Choose the correct answer below.
O A. The sample was not large enough to make a conclusion.
O B. At the 1% significance level, there is not enough evidence that the students' critical reading scores improved the second time they took the test.
OC. At the 1% significance level, there is enough evidence that the students' critical reading scores improved the second time they took the test.
O D. At the 1% significance level, there is evidence that the students' critical reading scores got worse the second time they took the test.

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