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...


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.

























































































345749427
767336777
663451787
454711544
453330718
462585658
550576773
572629591
481574510
628532411
702640686
608510509
617576546
392512573
794690581
527329451
666377720


(a)


Compute the mean, variance, and standard deviation of the GMAT scores for the 51 observations. (Round your answers to two decimal places.)

x= (  )


s
2=(  )


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 <>

H0: σ2 > 14,650

Ha: σ2 ≤ 14,650


H0: σ2 <>

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 thep-value. (Round your answer to four decimal places.)


p-value =


What is your conclusion?


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

Do not rejectH
0. We can conclude the variance in GMAT scores differs from the general population of GMAT takers.

RejectH
0. We can conclude the variance in GMAT scores differs from the general population of GMAT takers.

RejectH
0. We cannot conclude the variance in GMAT scores differs from the general population of GMAT takers.



Jun 03, 2022
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