Question

Suppose that in a certain year, it was reported that the variance in GMAT scores was...

Suppose that in a certain year, it was reported that the variance in GMAT scores was 14,630. 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
765 336 777
663 451 787
452 711 544
453 330 718
462 587 658
550 576 773
572 629 591
481 574 510
628 532 411
702 640 686
608 510 509
617 574 546
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 > 14,630

Ha: σ2 ≤ 14,630

H0: σ2 = 14,630

Ha: σ2 ≠ 14,630

    

H0: σ2 < 14,630

Ha: σ2 ≥ 14,630

H0: σ2 ≤ 14,630

Ha: σ2 > 14,630

H0: σ2 ≥ 14,630

Ha: σ2 < 14,630

(C) Use α = 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.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a) = 569.53

s2 = 16667.12

s = 129.10

b) H0: = 14630

H1: 14630

c) The test statistic = (n - 1)s2/

= 50 * 16667.12/14630

= 56.962

P-value = 2 * P( > 56.962)

= 2 * 0.2320 = 0.4640

Since the p-value is greater than the significance level, so we should not reject the null hypothesis.

Do not reject H0. We cannot conclude the variance in GMAT scores differs from the general population of GMAT takers.

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