A college preparation academy claims that their 3-hour crash course may have an effect on students' SAT scores. A skeptical parent decided to perform research and administered the practice SAT tests to a sample of 33 students the day before and the day after the advertised 3-hour crash course. The following data with the means and standard deviations were obtained: After: 523 537 601 641 514 596 605 631 624 528 591 604 573 684 576 577 596 585 597 592 603 564 544 517 642 689 608 591 577 546 615 607 638 (Note: The average and the standard deviation of the data are respectively 591.39 points and 42.91 points.) Before: 571 701 544 603 713 692 684 673 596 513 557 683 679 676 645 605 690 670 641 642 576 562 657 635 565 606 583 507 582 651 639 606 628 (Note: The average and the standard deviation of the data are respectively 623.48 points and 55.45 points.) Difference: -48 -164 57 38 -199 -96 -79 -42 28 15 34 -79 -106 8 -69 -28 -94 -85 -44 -50 27 2 -113 -118 77 83 25 84 -5 -105 -24 1 10 (Note: The average and the standard deviation of the data are respectively -32.09 points and 71.18 points.) Use 1% level of significance to decide whether there is sufficient evidence that the mean practice SAT score after the crash course is the same as the mean practice SAT score before the crash course. Procedure: Assumptions: (select everything that applies) Normal populations Independent samples Population standard deviation are unknown but assumed equal Simple random samples The number of positive and negative responses are both greater than 10 for both samples Population standard deviations are known Sample sizes are both greater than 30 Population standard deviation are unknown Paired samples

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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Question

A college preparation academy claims that their 3-hour crash course may have an effect on students' SAT scores. A skeptical parent decided to perform research and administered the practice SAT tests to a sample of 33 students the day before and the day after the advertised 3-hour crash course. The following data with the means and standard deviations were obtained:

After:

523	537	601	641	514
596	605	631	624	528
591	604	573	684	576
577	596	585	597	592
603	564	544	517	642
689	608	591	577	546
615	607	638

(Note: The average and the standard deviation of the data are respectively 591.39 points and 42.91 points.)

Before:

571	701	544	603	713
692	684	673	596	513
557	683	679	676	645
605	690	670	641	642
576	562	657	635	565
606	583	507	582	651
639	606	628

(Note: The average and the standard deviation of the data are respectively 623.48 points and 55.45 points.)

Difference:

-48	-164	57	38	-199
-96	-79	-42	28	15
34	-79	-106	8	-69
-28	-94	-85	-44	-50
27	2	-113	-118	77
83	25	84	-5	-105
-24	1	10

(Note: The average and the standard deviation of the data are respectively -32.09 points and 71.18 points.)

Use 1% level of significance to decide whether there is sufficient evidence that the mean practice SAT score after the crash course is the same as the mean practice SAT score before the crash course.

Procedure:

Assumptions: (select everything that applies)

Normal populations
Independent samples
Population standard deviation are unknown but assumed equal
Simple random samples
The number of positive and negative responses are both greater than 10 for both samples
Population standard deviations are known
Sample sizes are both greater than 30
Population standard deviation are unknown
Paired samples

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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