ROBERT M. PARKER, Circuit Judge:

I. PROCEEDINGS BELOW

Mona Miller filed an age discrimination action against Butcher Distributors under the Age Discrimination in Employment Act, 29 U.S.C. § 621 et seq. After the jury awarded Miller a judgment of $45,000, the district court granted Butcher Distributors’ motion for judgment as a matter of law and conditionally granted Butcher Distributors’ motion for a new trial. Miller timely appealed.

II. ANALYSIS

The district court granted the defendant’s motion for judgment as a matter of law on the grounds that Miller did not establish a prima facie case and that she did not adduce any direct evidence of discrimination based upon her age. This court reviews a district court’s grant of judgment as a matter of law de novo and affirms only if the facts and inferences are so strong and overwhelming that a reasonable jury could not arrive at a contrary verdict. E.E.O.C. v. Louisiana Office of Community Servs., 47 F.3d 1438, 1443 (5th Cir.1995). If reasonable minds might reach different conclusions, the motion for judgment as a matter of law should be denied and the case submitted to the jury. Id.

Butcher Distributors supports the judgment as a matter of law on two grounds. First, it argues that Miller did not make out a prima facie case. Specifically, Butcher Distributors argues that (1) Miller was not qualified for the position, (2) she was not terminated from her employment, and (3) she was not replaced. Second, Butcher supports the judgment as a matter of law by arguing that Miller failed to satisfy her burden of persuasion in regard to rebutting the proffer of a legitimate, non-discriminatory reason for termination.

*267 “When an employment discrimination ease reaches the fact finder, the pertinent inquiry is whether the plaintiff has proven discrimination, not whether he has made a prima facie case.” Shattuck v. Kinetic Concepts, Inc., 49 F.3d 1106, 1110 (5th Cir.1995). Therefore, Butcher Distributors’ first argument is essentially that the evidence was insufficient to support the jury verdict for Miller. See Weaver v. Amoco Prod. Co., 66 F.3d 85, 87 (5th Cir.1995).

In this regard, Butcher Distributors argues that the only evidence offered to show discrimination was Miller’s self-serving testimony and that the district court properly disregarded such testimony in deciding that the evidence was insufficient to support the jury verdict. See Ralston Purina Co. v. Hobson, 554 F.2d 725 (5th Cir.1977). However, Butcher Distributors misapplies Ral-ston. Miller’s testimony was not “naturally impossible,” as was the case in Ralston. See Dotson v. Clark Equip. Co., 783 F.2d 586, 588 (5th Cir.1986). Whether or not Miller was qualified for the job was hotly disputed, and the parties attempted to produce evidence to support both views. We must examine the record to determine if a reasonable jury could have reached the same verdict.

There is no dispute that Miller, who was 57 years old at the time of her departure from Butcher Distributors, was within the protected class. However, Butcher Distributors for the first time now argues, somewhat inanely, that Miller was not actually terminated from employment. Instead, the defendant contends that Miller was offered a part-time position which she refused. Thus, Butcher Distributors asserts that Miller voluntarily resigned.

In its order granting the judgment as a matter of law, the district court wrote that “[t]he defendants have claimed throughout this proceeding that the reason Miller was terminated was her inability to acquire the computer skills necessary to perform her job” (emphasis added). Butcher Distributors did not challenge the district court’s finding. The failure to file a cross appeal in a timely manner as mandated by Rule 4 of the Federal Rules of Appellate Procedure precludes Butcher Distributors from now raising this argument. “[Wjithout the filing of a cross-appeal, an appellee ‘may not attack the decree with a view either to enlarging his own rights thereunder or of lessening the rights of his adversary, whether what he seeks is to correct an error or to supplement the decree with respect to a matter not dealt with below.’” Robicheaux v. Radcliff Material, Inc., 697 F.2d 662, 668 (5th Cir.1983), quoting, Morley Constr. Co. v. Maryland Casualty Co., 300 U.S. 185, 191, 57 S.Ct. 325, 328, 81 L.Ed. 593 (1937).

Furthermore, even if Butcher Distributors had properly raised this argument, we find no merit in it. The evidence presented at trial allowed the jury to conclude that Miller was terminated from Butcher Distributors. Specifically, Miller testified that William Hanesworth, a Butcher Distributors manager and Miller’s boss, told her, “It’s either part time, or you’re out of here.” Clearly, Miller was at the very least constructively terminated. See Barrow v. New Orleans S.S. Assoc., 10 F.3d 292 (5th Cir.1994) (reduction in job responsibilities may constitute constructive discharge if a reasonable employee would feel compelled to resign).

Butcher Distributors also argues that Miller was not replaced. Following Miller’s departure, Butcher Distributors hired Dana Sullivan, an individual who was approximately 25 years old. Sullivan, who unlike Miller had a Masters of Business Administration degree, assumed Miller’s job duties. Furthermore, Hanesworth testified that Sullivan “replaced” Miller. The evidence was thus sufficient for the jury to conclude that Miller was replaced.

The key question in this appeal is whether Miller was qualified. Miller attended at least four classes at Butcher Distributors’ expense in order to learn the necessary computer skills to successfully perform her duties. Miller testified that following these classes she was able to operate Lotus and WordPer-fect. Miller testified that she revised the price lists using Lotus, and Hanesworth testified that Miller did complete some projects to his satisfaction.

On the other hand, Miller admitted that she was not completely confident using the *268 computer and wanted to become more proficient. On cross-examination, Miller could not answer basic questions regarding how to operate certain computer software programs. Additionally, Hanesworth testified that Miller was simply not capable of doing the computer work that he wanted her to do some two and a half years after he first asked her to learn the skills. Tammy Briscoe, Miller’s co-worker, testified that Miller was woefully inadequate in computer capabilities and repeatedly pestered her with basic questions, causing Briscoe to complain to Hanesworth about the interruptions. Finally, in a 1991 letter to Hanesworth, Miller admitted that she still did not have the computer skills that Hanesworth had asked her to obtain.

“[I]t is the function of the jury as the traditional finder of facts, and not the court, to weigh conflicting evidence and inferences, and to determine the credibility of witnesses.” Boeing Co. v. Shipman, 411 F.2d 365, 375 (5th Cir.1969) (en banc). However, “[tjhere must be a conflict in substantial evidence to create a jury question.” Id. Substantial evidence is defined as “evidence of such quality and weight that reasonable and fair-minded men [or women] in the exercise of impartial judgment might reach different conclusions.” Id. at 374.

The question of whether there is enough substantial evidence to support the jury’s finding that Miller was qualified for the job is a close one. However, we agree with the district court that on the facts of this case a reasonable jury could not conclude that Butcher Distributors terminated Miller for any reason other than her lack of qualifications.

The granting of the judgment as a matter of law is therefore AFFIRMED.