Suppose that in a certain year, it was reported that

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.

(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.