Suppose that in a certain year, it was reported that the variance in GMAT scores was 14,670. 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
452	711	544
453	330	718
462	587	658
550	576	773
572	629	591
481	574	510
628	532	411
702	640	686
606	510	509
617	576	546
392	512	573
794	690	581
525	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.)

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 ≤ 14,670
• H_a: σ² > 14,670
• H₀: σ² ≥ 14,670
• H_a: σ² < 14,670
• H₀: σ² = 14,670
• H_a: σ² ≠ 14,670
• H₀: σ² > 14,670
• H_a: σ² ≤ 14,670
• H₀: σ² < 14,670
• H_a: σ² ≥ 14,670

(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.)

What is your conclusion?

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

Answer rating: 100% (QA)

a Sample Mean 56650 Sample Variance 1664029 Sample SD ... View the full answer