Suppose that in a certain year, it was reported that the variance in GMAT scores was 14,650. At a recent summit, a group of economics professors met to discuss the GMAT performance of undergraduate students majoring in economics. Some expected the variability in GMAT scores achieved by undergraduate economics students to be greater than the variability in GMAT scores of the general population of GMAT takers. However, others took the opposite view. Suppose the following are GMAT scores for 51 randomly selected undergraduate students majoring in economics. 345 749 427 767 336 777 663 451 787 454 711 544 453 330 718 462 585 658 550 576 773 572 629 591 481 574 510 628 532 411 702 640 686 608 510 509 617 576 546 392 512 573 794 690 581 527 329 451 666 377 720 (a) Compute the mean, variance, and standard deviation of the GMAT scores for the 51 observations. (Round your answers to two decimal places.) x= ( ) s2=( ) s= ( ) (b) Develop hypotheses to test whether the sample data indicate that the variance in GMAT scores for undergraduate students majoring in economics differs from the general population of GMAT takers. H0: σ2 = 14,650 Ha: σ2 ≠ 14,650 H0: σ2 ≥ 14,650 Ha: σ2 < 14,650 H0: σ2 > 14,650 Ha: σ2 ≤ 14,650 H0: σ2 < 14,650 Ha: σ2 ≥ 14,650 H0: σ2 ≤ 14,650 Ha: σ2 > 14,650 (c) Use ? = 0.05 to conduct the hypothesis test formulated in part (b). Find the value of the test statistic. (Round your answer to three decimal places.) ( ) Find the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? Do not reject H0. We cannot conclude the variance in GMAT scores differs from the general population of GMAT takers. Do not reject H0. We can conclude the variance in GMAT scores differs from the general population of GMAT takers. Reject H0. We can conclude the variance in GMAT scores differs from the general population of GMAT takers. Reject H0. We cannot conclude the variance in GMAT scores differs from the general population of GMAT takers.
Suppose that in a certain year, it was reported that the variance in GMAT scores was 14,650. At a recent summit, a group of economics professors met to discuss the GMAT performance of undergraduate students majoring in economics. Some expected the variability in GMAT scores achieved by undergraduate economics students to be greater than the variability in GMAT scores of the general population of GMAT takers. However, others took the opposite view. Suppose the following are GMAT scores for 51 randomly selected undergraduate students majoring in economics. 345 749 427 767 336 777 663 451 787 454 711 544 453 330 718 462 585 658 550 576 773 572 629 591 481 574 510 628 532 411 702 640 686 608 510 509 617 576 546 392 512 573 794 690 581 527 329 451 666 377 720 (a) Compute the mean, variance, and standard deviation of the GMAT scores for the 51 observations. (Round your answers to two decimal places.) x= ( ) s2=( ) s= ( ) (b) Develop hypotheses to test whether the sample data indicate that the variance in GMAT scores for undergraduate students majoring in economics differs from the general population of GMAT takers. H0: σ2 = 14,650 Ha: σ2 ≠ 14,650 H0: σ2 ≥ 14,650 Ha: σ2 < 14,650 H0: σ2 > 14,650 Ha: σ2 ≤ 14,650 H0: σ2 < 14,650 Ha: σ2 ≥ 14,650 H0: σ2 ≤ 14,650 Ha: σ2 > 14,650 (c) Use ? = 0.05 to conduct the hypothesis test formulated in part (b). Find the value of the test statistic. (Round your answer to three decimal places.) ( ) Find the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? Do not reject H0. We cannot conclude the variance in GMAT scores differs from the general population of GMAT takers. Do not reject H0. We can conclude the variance in GMAT scores differs from the general population of GMAT takers. Reject H0. We can conclude the variance in GMAT scores differs from the general population of GMAT takers. Reject H0. We cannot conclude the variance in GMAT scores differs from the general population of GMAT takers.
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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Suppose that in a certain year, it was reported that the variance in GMAT scores was 14,650. At a recent summit, a group of economics professors met to discuss the GMAT performance of undergraduate students majoring in economics. Some expected the variability in GMAT scores achieved by undergraduate economics students to be greater than the variability in GMAT scores of the general population of GMAT takers. However, others took the opposite view. Suppose the following are GMAT scores for 51 randomly selected undergraduate students majoring in economics.
| 345 | 749 | 427 |
| 767 | 336 | 777 |
| 663 | 451 | 787 |
| 454 | 711 | 544 |
| 453 | 330 | 718 |
| 462 | 585 | 658 |
| 550 | 576 | 773 |
| 572 | 629 | 591 |
| 481 | 574 | 510 |
| 628 | 532 | 411 |
| 702 | 640 | 686 |
| 608 | 510 | 509 |
| 617 | 576 | 546 |
| 392 | 512 | 573 |
| 794 | 690 | 581 |
| 527 | 329 | 451 |
| 666 | 377 | 720 |
(a)
Compute the mean, variance, and standard deviation of the GMAT scores for the 51 observations. (Round your answers to two decimal places.)
x= ( )
s2=( )
s= ( )
(b)
Develop hypotheses to test whether the sample data indicate that the variance in GMAT scores for undergraduate students majoring in economics differs from the general population of GMAT takers.
H0: σ2 = 14,650
Ha: σ2 ≠ 14,650
H0: σ2 ≥ 14,650
Ha: σ2 < 14,650
H0: σ2 > 14,650
Ha: σ2 ≤ 14,650
H0: σ2 < 14,650
Ha: σ2 ≥ 14,650
H0: σ2 ≤ 14,650
Ha: σ2 > 14,650
(c)
Use ? = 0.05 to conduct the hypothesis test formulated in part (b).
Find the value of the test statistic. (Round your answer to three decimal places.)
( )
Find the p-value. (Round your answer to four decimal places.)
p-value =
What is your conclusion?
Do not reject H0. We cannot conclude the variance in GMAT scores differs from the general population of GMAT takers.
Do not reject H0. We can conclude the variance in GMAT scores differs from the general population of GMAT takers.
Reject H0. We can conclude the variance in GMAT scores differs from the general population of GMAT takers.
Reject H0. We cannot conclude the variance in GMAT scores differs from the general population of GMAT takers.
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