Greaney, J.
The defendant was convicted of murder in the first degree (by reason of deliberate premeditation) of his wife. Represented by new counsel on appeal, he raises twelve arguments in seeking relief from the conviction and from the denial of his motion for postconviction relief under Mass. R. Crim. P. 30 (a) and (b), 378 Mass. 900 (1979). The defendant’s principal contentions concern the denial of his motion to dismiss the indictment for the alleged failure of the Commonwealth’s investigators to conduct a proper investigation; the denial of his motion to continue the trial so further deoxyribonucleic acid (DNA) testing could be done; the denial of his motions to suppress which challenged a warrantless entry by the police into the marital home and evidence seized thereafter pursuant to search warrants; the admission of evidence of prior bad conduct and of the victim’s state of mind; the judge’s instructions to the jury; and alleged bias on the part of one juror. We affirm the defendant’s conviction and the order denying his motion for postconviction relief. We discern no reason to exercise our authority under G. L. c. 278, § 33E, either to reduce the verdict or to order other relief.
[768]*768The jury could have found the following facts. The defendant and the victim lived together at their home at 1051 Putnam Avenue Extension, Marstons Mills. In the early evening hours of March 16, 1995, the victim obtained a protective order against the defendant under G. L. c. 209A, and, at the same time, a Barnstable police officer obtained an arrest warrant for him on charges that he threatened to murder the victim and bum down their home. After the G. L. c. 209A order and the arrest warrant were finalized, the police went to the home with the victim and arrested the defendant who, when he was placed under arrest, told the police, “This is fucking bullshit.” The defendant also made derogatory remarks about the victim which were false. Later on the night of March 16, the defendant posted bail and checked into a local hotel for a one-night stay. There was no precise record of when the defendant checked out of the hotel.
Early on the morning of March 17, the defendant’s truck was seen parked in front of the marital home by a neighbor who was walking his dog. The neighbor then heard the truck start up and saw the defendant driving it. The neighbor had never seen the defendant leave his house so early in the morning, and the neighbor noticed that the defendant drove away on a route which the neighbor had not seen him use before. The neighbor fixed the time of the defendant’s departure at slightly before 6:30 a.m.
Around noon on March 17, the defendant spoke with a witness. The defendant seemed very calm. He told the witness that the court system can cause a major problem between husband and wife, that he had put the victim up on a pedestal after marrying her and did not want her working two jobs, that he and the victim were having a conflict which had reached the point that required the defendant to leave their home, and that, after he had left, the victim had called the police. Later on the afternoon of March 17, the defendant went to the clerk’s office of the Barnstable District Court seeking to have the G. L. c. 209A order against him removed. The defendant told an assistant clerk that the entry of the order had been a misunderstanding. The defendant’s demeanor during the conversation was described as “[djetermined.”
The victim’s daughter last spoke with her mother on March 15. Between March 16 and March 18, the victim’s daughter [769]*769tried to contact her mother on the telephone several times. The telephone at the victim’s home would ring, but the answering machine did not engage. After speaking with family members on March 18, the victim’s daughter telephoned the police expressing concerns about her mother’s well-being.
The victim’s son also had tried to telephone his mother repeatedly and became concerned when she did not answer his calls or telephone him. He took note of her failure to respond to messages, inviting her to his home to celebrate his wife’s birthday, and of her failure to call to wish his wife a happy birthday. The victim’s son went to his mother’s home twice on March 17, and received no response to his attempts to enter. He saw the victim’s car in the driveway. On March 18, the victim’s son drove past his mother’s home and saw her car parked where it had been located the previous day.
As a result of telephone calls by the victim’s family, a Barnstable police officer went to the home to check on the well-being and safety of the victim. The officer obtained no response when he knocked, and he saw that all the windows and doors of the house were locked. The officer entered the home by pushing aside a frame covering the entrance to the cellar; he looked for the victim, and shortly after his entry, the officer found her dead in one of the upstairs bedrooms. During a later search of the perimeter of the home, the officer noticed that the wires in the telephone junction box had been pulled away from their terminals. This condition of the wires would cause persons calling the victim to hear a ringing at their end of the line, but the call would not ring through, and anyone picking up the telephone inside the house would not get a dial tone.
The medical examiner determined that the victim had died as a result of asphyxia due to smothering. The examiner observed seventeen injuries on the victim’s body which were inflicted contemporaneously or within minutes of the time of her death. The examiner placed the probable time of death between the hours of 11 p.m. on March 16, and 6:30 a.m. on March 17.
The jury could also have found that a hostile relationship existed between the defendant and the victim. In September, 1993, they had argued violently and the victim sought help from a neighbor after the defendant attempted to choke her and smother her. In 1994, the defendant and the victim had argued [770]*770again. The victim expressed anger toward the defendant, and he told her, “If I can’t have you, nobody will.”1
The defendant maintained that the police had not properly investigated the case and neglected to gather evidence that might have exculpated him. He attacked the credibility of the Commonwealth’s witness who placed him at the marital home early on the morning of March 17. He suggested that the victim may have died from natural causes. The defendant also claimed that he did not go near the marital home after he had been arrested, and that his presence elsewhere could be accounted for during all critical times.
1. The defendant filed a pretrial motion to dismiss the indictment, asserting that “the Commonwealth, at every stage, failed to follow reasonable procedures in conducting the investigation in this case, and failed to conduct appropriate tests, and as a result, destroyed any opportunity for the discovery of exculpatory evidence.” He points to instances during the investigation, that, he says, indicate that the Commonwealth’s investigators contaminated the crime scene. As a result, he claims it was made difficult, or impossible, to recover fingerprints or to obtain other materials (such as fibers or hairs) that, after testing, might have excluded him as a suspect. He maintains that the police deviated from guidelines and failed to preserve material evidence when they destroyed their handwritten notes. He asserts also that the medical examiner failed to conduct tests on an inhalator found by the victim’s bedside or to investigate matters that may have shed light on whether the victim died from a natural cause, namely cardiac arrhythmia.
The judge conducted an evidentiary hearing, and to support his denial of the motion made findings of fact. There is no need to detail the judge’s findings. They more than adequately support his conclusion that “there is no basis for the [defendant’s] contention that the Commonwealth intentionally destroyed evidence . . . [and] no evidence of bad faith or negligence by the Commonwealth in connection with the gathering and preserving of evidence.” The judge also appropriately observed [771]*771that the defendant’s criticisms of the police investigation were an “attempt to turn a simple negative into active wrongdoing,” and that the defendant’s contentions lacked factual support in the record.2 We add three other points:
(a) The Barnstable police officer, who was dispatched to the marital home, initially did not follow crime scene guidelines because those guidelines would not be followed when the police are checking on the well-being of a person.
(b) The medical examiner’s opinion as to the cause of death was supported by independent medical evidence of injuries to the victim, all which excluded any probability of death by natural causes including cardiac arrhythmia.
(c) The handwritten notes compiled by the police were destroyed in keeping with normal procedures after police reports based on the notes were completed.
We conclude that the defendant did not establish a reasonable likelihood, based on concrete information rather than speculation, that the investigation could have produced evidence favorable to his case. Commonwealth v. Olszewski, 401 Mass. 749, 754 (1988), S.C., 416 Mass. 607 (1993). There was no error in the denial of the motion to dismiss.
2. The judge properly denied the defendant’s motion, filed about ten days before the commencement of the trial, to continue the case to permit further DNA testing on hairs found on the blanket used to cover the victim’s body. (Testing had previously determined that some hairs recovered from the blanket were consistent with the victim’s hair, and that seminal fluid on the blanket probably came from the defendant).
The judge held a hearing on the motion. The motion was filed late, and the judge appropriately considered it dilatory. The onus was on the defendant to explain the delay and to establish a need for further testing. There was no basis provided in the testimony of the defendant’s chemist (or elsewhere in his evidence) to indicate that further testing of hairs found on the [772]*772blanket might furnish exculpatory evidence.3 The judge properly concluded as follows: “considering that the date set for trial is [about] one week [away], I find nothing in the materials supplied to me that would permit a continuance of the trial for the purposes of additional DNA testing. Not only do the materials fail to demonstrate that such testing is reasonably likely to furnish evidence of value to the defendant, but additionally, it is apparent that whatever belief to that effect existed, that belief was every bit as apparent [at an earlier date]. If the defendant had desired to pursue the answer at that time, [the testing] could have been done along with the other tests that were authorized.”
3. In his opening statement, the prosecutor said the following to the jury about the defendant:
“And when confronted by the police and informed by the police of the reason that numerous police were surrounding him to arrest him, he was told that, you’re being arrested for the murder of your wife. And he said nothing except, I was in Connecticut. Not a word about his wife, the person who knew nothing.”
The defendant’s trial counsel objected, and the judge (after a bench conference) let the remarks stand. It is now argued that the statement impermissibly trenched on the defendant’s right to remain silent after his arrest, an error, the defendant goes on to claim, that was compounded by the prosecutor’s examination of police witnesses about the defendant’s statements and conduct at the time of his arrest.
There is no merit to the argument. At the time of his arrest the defendant was given, and understood, his Miranda rights. Thereafter, he engaged in conversation with the police concerning his whereabouts, the victim, and several other topics. It is clear (as the judge had earlier found) that the defendant had understood and had voluntarily waived his Miranda rights. The [773]*773situation was one in which the defendant sought to deflect attention from himself, and perhaps establish an alibi. The defendant’s statements (and failure to inquire about his wife) were appropriate matters for comment and exploration.
4. The defendant moved to suppress any evidence obtained by the police after a warrantless entry into the marital home. The judge conducted an evidentiary hearing on the motion, made findings of fact, and concluded that the entry was constitutionally proper under the so-called emergency exception to the general rule that a warrant is necessary before police enter a dwelling without the occupant’s consent.
The judge found that Sergeant John Sweeney of the Barn-stable police department dispatched Officer Robert Cogeschall on March 18, 1995, to the marital home to check on the victim’s well-being. Sergeant Sweeney was aware that the defendant had been arrested on March 16 for threats against the victim to commit murder and burn the marital home, and that the defendant has been released on bail. Sweeney had received several telephone calls from the victim’s son, daughter, and brother expressing concern about the victim’s well-being. The victim’s car was at the marital home, but she had not responded to her son’s attempt to contact her. Sweeney sent Officer Coge-schall to the marital home within minutes of his receipt of this information.
Officer Cogeschall arrived at the marital home within fifteen minutes of his dispatch. He was also aware that threats had been made against the victim, and that she had not been heard from in a couple of days. When Cogeschall arrived at the home, he had not made arrangements to be met there by someone with a key. No one responded to Cogeschall’s knocks on the door. In checking the house, Cogeschall observed that the doors were locked and all the windows were secure. Cogeschall obtained permission from Sergeant Sweeney to enter the home through the cellar by pushing aside a frame at the bottom of the cellar stairs. Cogeschall went from the basement to the first floor. He noted that the house was exceptionally warm, and that the door to the oven was partially open. When he could not find the victim, Cogeschell went to the second floor where he found her dead in a bedroom.
Cogeschall attempted to use the telephone in the kitchen to advise Sergeant Sweeney of his discovery, but found it inoperable. He then observed that all the burners on the stove were [774]*774on, and that the temperature of the oven had been set at 350 degrees. Cogeschall finally made contact with Sergeant Sweeney from a cellular telephone and remained at the home to secure what was now considered to be a crime scene. Shortly thereafter, the victim’s son arrived at the home. Sergeant Sweeney had sent the son in the belief that the son had a key to the house. This information was not known to Cogeschall when he entered the home, and the son, in fact, did not have a key.
The law that the judge found applicable to these facts was summarized by the Appeals Court in Commonwealth v. Bates, 28 Mass. App. Ct. 217, 219-220 (1990), as follows:
“Unless this entry fell within ‘a well defined exception’ to the warrant requirement of the Fourth Amendment, it was a search ‘conducted outside the judicial process without prior approval by judge or magistrate’ and was ‘per se unreasonable.’ Thompson v. Louisiana, 469 U.S. 17, 20 (1984). The exception relied on by the Commonwealth is the ‘emergency’ exception which applies when the purpose of the police entry is not to gather evidence of criminal activity but rather, because of an emergency, to respond to an immediate need for assistance for the protection of life or property. ‘The need to protect or preserve life or avoid serious injury is justification for what would be otherwise illegal absent an exigency or emergency.’ Mincey v. Arizona, 437 U.S. [385,] 392 [(1978)], quoting from Wayne v. United States, 318 F.2d 205, 212 (D.C. Cir.), cert. denied, 375 U.S. 860 (1963). Commonwealth v. Kingsbury, 7 Mass. App. Ct. 51, 54, S.C., 378 Mass. 751 (1979). United States v. Barone, 330 F.2d 543, 545 (2d Cir.), cert. denied, 377 U.S. 1004 (1964). People v. Boyd, 123 Misc. 2d 634, 641 (N.Y. Sup. Ct. 1984), aff’d, 125 A.D.2d 1013 (N.Y. App. Div. 1987). Duquette v. Godbout, 471 A.2d 1359, 1362 (R.I. 1984). See generally 2 LaFave, Search and Seizure § 6.6(a) (2d ed. 1987 & Supp. 1989); Mascolo, The Emergency Doctrine Exception to the Warrant Requirement Under the Fourth Amendment, 22 Buffalo L. Rev. 419, 433-437 (1973); Model Code of Pre-Arraignment Procedure § SS 260.5 (1975). For the exception to apply, the burden of proof is on the Commonwealth to show that the warrantless entry falls within the exception and that there were reasonable grounds for the . . . police to [775]*775believe (an objective standard) that an emergency existed. Root v. Gauper, 438 F.2d 361, 364 (8th Cir. 1971). People v. Mitchell, 39 N.Y.2d 173, 177, cert. denied, 426 U.S. 953 (1976). 2 LaFave, Search and Seizure § 6.6(a), at 698.” (Footnote omitted.)
We agree with the judge that the situation facing the police justified entry into the house. There existed objectively reasonable grounds to believe that the victim might be injured or dead inside. The defendant had made a direct threat to murder the victim and bum down the house two days earlier, and he was at large. The victim had failed to respond to numerous attempts to reach her. The findings necessarily must be evaluated in the context of domestic violence which often calls for rapid police response designed to prevent further injury to a victim, to see whether a threat against a victim has been carried out, or to ascertain whether some other grave misfortune has befallen a victim.4 It is clear as well that the police believed that the victim was in the home, and that Cogeschall’s entry was not primarily motivated by an intent to search the home or to seize evidence.
In attacking the judge’s decision, the defendant refers to findings which are not supported by the evidence presented at the hearing on the motion to suppress.5 We have not considered these findings in reaching our conclusion that the facts summarized above, which are supported by the evidence, justify the application of the emergency exception to the warrant rule.
The defendant also refers to evidence at the trial that the police were aware of family concerns about the victim on March 17, the day before Officer Cogeschall was sent to the marital [776]*776home. He suggests that the evidence was improperly withheld at the hearing on the motion to suppress, and that it establishes that an emergency did not exist because the police had already known for over twenty-four hours that the victim’s family was concerned about her.
There is nothing to show that the Commonwealth acted improperly at the hearing on the motion to suppress. The defendant’s trial counsel did not move during the trial to have the judge reconsider his ruling on the motion to suppress in light of the evidence that is now argued to us. We do not place the same emphasis on the evidence that the defendant does. We think that, if anything, the evidence supports the existence of an emergency on March 18, when Officer Cogeschall was sent to the marital home. The police could have reasonably thought that the victim might respond to attempts to reach her, so that action on their part on March 17 would be premature. One day later, however, repeated attempts to reach the victim had been unsuccessful, and the need for immediate action in view of the defendant’s threats was much more acute.6 The motion to suppress was properly denied.7
5. The defendant argues that the judge should have suppressed evidence obtained pursuant to search warrants. His argument rests on the premise that the warrantless entry into the marital home discussed above was unlawful, and, as a consequence, the affidavits supporting the search warrant are deficient under the fruit of the poisonous tree doctrine expressed in Wong Sun v. United States, 371 U.S. 471, 488 (1963). The argument fails in [777]*777view of our conclusion that the entry by Officer Cogeschall was proper.
6. (a) The defendant’s trial counsel objected to testimony by a neighbor of the victim that, in September, 1993, the victim had gone to the neighbor’s house for help after the defendant had tried to kill her by choking her and smothering her with a pillow.
We agree with the judge’s ruling that the testimony was admissible under the spontaneous utterance exception to the hearsay rule. The evidence heard by the judge at the voir dire warranted conclusions that the victim sought the neighbor’s assistance between 10 p.m. and 10:30 p.m., on September 5, 1993, immediately after the incident occurred and while highly distraught, suffering from visible injuries, and under the influence of the exciting event. See Commonwealth v. Whelton, ante 24, 26 (1998), and cases cited.
We reject the defendant’s arguments that the evidence constituted impermissible “bad act” evidence. The judge carefully considered the arguments made by the defendant’s trial counsel to exclude the evidence, and the judge had discretion in weighing its probative value against its prejudicial effect. The evidence was admissible to show the defendant’s motive and intent and to depict the existence of a hostile relationship between the defendant and the victim. We explained the general principles in this area in Commonwealth v. Cormier, 427 Mass. 446, 450 (1998), as follows:
“ Tt is well settled that the prosecution may not introduce evidence that a defendant has previously misbehaved, in-dictably or not, for the purposes of showing his bad character or propensity to commit the crime charged, but such evidence may be admissible if relevant for some other purpose.’ Commonwealth v. Helfant, 398 Mass. 214, 224 (1986). ‘Evidence of a hostile relationship between a defendant and his spouse may [however] be admitted as relevant to the defendant’s motive to the kill the victim spouse.’ Commonwealth v. Gil, 393 Mass. 204, 215 (1984). A defendant’s oral threats and repeated acts of violence may indicate ‘settled ill-will towards his wife, and therefore [bear] directly on the question whether there was any motive for him to commit the crime.’ Commonwealth v. Holmes, 157 Mass. 233, 240 (1892). See Commonwealth [778]*778v. Rodriguez, 425 Mass. 361, 370-371 (1997); Commonwealth v. Gil, supra at 215-216; Commonwealth v. Fitzgerald, 380 Mass. 840, 850 (1980); Commonwealth v. Bonomi, 335 Mass. 327, 343 (1957).”
The evidence satisfied these principles.
The judge also gave the jury a limiting instruction to reduce the possible prejudicial effect of the evidence. He told the jury that the evidence could not be used to show that the defendant had a bad character or a propensity to have committed the murder. He also advised them that the evidence could not be used to establish the identity of the killer. The judge indicated that the evidence could be considered as revealing the nature of the relationship between the defendant and the victim and to show motive and intent on the defendant’s part.8
(b) The victim’s daughter testified to an argument she overheard between the defendant and the victim in September, 1994. The argument concerned the defendant’s repeated absences from the home. The victim indicated that the defendant was being “irrational and ridiculous, and she was fed up.” The victim described the defendant as “[djishonest,” a “[l]iar,” “[cjheating,” and said that she “had had enough.” The defendant told the victim that, “If I can’t have you, nobody will.”
The evidence was admissible to show the relationship between the defendant and the victim. “A murder victim’s attitude of contempt or hostility toward the defendant, when it is known to the defendant . . . might warrant a fact finder’s determination that the defendant responded by killing the victim.” Commonwealth v. Qualls, 425 Mass. 163, 168 (1997). Cf. Commonwealth v. Jenner, 426 Mass. 163, 164-166 (1997). The victim’s statement also explained, and put in context, the defendant’s response. Prior to the testimony, the judge gave a limiting instruction to the jury which clarified the purpose of the evidence and the restrictions on its consideration.
7. There is no merit to the defendant’s argument that the prosecutor asked the medical examiner an improper hypothetical question. The question was posed on redirect examination to [779]*779respond to matters that had been raised by the defendant’s trial counsel as to the cause of the victim’s death. The facts in the question had a basis in the evidence and did not call on the medical examiner to render an opinion as to the defendant’s possible guilt. The medical examiner’s response was that the victim’s injuries were “consistent with” the facts described by the prosecutor which included facts pertaining to the defendant’s height and weight. See Commonwealth v. Woods, 419 Mass. 366, 374, 375 n.13 (1995); Commonwealth v. Allen, 395 Mass. 448, 458-459 (1985).
8. The decision whether to instruct the jury about the claimed failure of the police to conduct an adequate investigation and to conduct forensic tests was within the judge’s discretion. Commonwealth v. Rivera, 424 Mass. 266, 274 (1997), cert. denied, 119 S. Ct. 346 (1998). The defendant’s trial counsel examined the Commonwealth’s witnesses about the quality of the investigation and the perceived need for testing, and he argued the defendant’s position on the alleged deficiencies to the jury in his closing argument. There was nothing to demonstrate that the Commonwealth’s investigation or failure to test was unreasonable or calculated to deprive the defendant of potentially exculpatory evidence. Id. The judge did not err by declining to give the instruction.
9. The defendant requested that the jury be instructed only on murder in the first degree, and the Commonwealth acquiesced in this request. The judge conducted a colloquy with the defendant. Contrary to the defendant’s present assertions, we are satisfied that he (a) was made aware of the differences between murder in the first and second degrees, (b) knew that a conviction of the latter could lead to eligibility for parole in fifteen years, although parole would not be guaranteed, (c) had discussed the matter with his trial counsel, (d) was acting voluntarily, and (e) was motivated by the desire to have a complete acquittal or nothing, because, as the defendant put it, “Basically, the way I look at it, the Commonwealth is trying to charge me for the death of my wife which I didn’t do, Your Honor.” This argument now made by the defendant that the jury should have been instructed on second degree murder, is foreclosed by our decision in Commonwealth v. Vinnie, ante 161, 179-181, cert. denied, 119 S. Ct. 523 (1998).
10. The defendant’s motion for postconviction relief claimed that his trial counsel had furnished him with ineffective as[780]*780sistance of counsel in several respects. We have examined his contentions under the standard that governs ineffective assistance claims in a case where there has been a conviction of murder in the first degree. See Commonwealth v. Parker, 420 Mass. 242, 245-246 (1995). The judge acted correctly in rejecting the claims summarily in his memorandum of decision. The defendant was not harmed by his trial counsel’s failure to locate a witness who might verify the time he checked out of the local hotel. The information was brought out through other witnesses, and, this witness, if he could be located at all, would only marginally aid the defense. The claim that his trial counsel employed an investigator who did not do a proper job for the defense is pure speculation. For the reasons already discussed, the defendant’s trial counsel did nothing that could have harmed the defendant in connection with the defendant’s informal decision to have the jury instructed only on murder in the first degree or in connection with the hypothetical question posed by the prosecutor on redirect examination of the medical examiner. From all that appears in the record, the defendant’s trial counsel provided him with a thorough and vigorous defense.
11. The defendant argues that the judge should have held an evidentiary hearing with respect to his allegation in his motion for postconviction relief that a juror knew him, and failed to disclose that fact to the judge, and that the juror had had a confrontation with the defendant on a prior occasion (implying that the juror harbored hostility toward him).
The judge correctly decided, for the reasons given in his memorandum of decision, that the defendant’s claim of possible juror bias was not supported by the record of empanelment and rested on speculation. The juror made no affirmative response to general questions posed to the jury venire and responded positively and forthrightly to questions posed to him when he was examined individually by the judge. It appears that the defendant actively participated with his trial counsel in the selection of the jury. The defendant may have wanted the juror to sit because he desired to exclude as many women from the jury as possible,9 and because the defense may have thought the juror would favor the defendant’s claim of police misconduct in [781]*781view of the juror’s disclosure that he had a criminal record. The affidavit furnished by the defendant indicated only that the juror may have known the defendant, and that the affiant saw the two men speak to each other briefly at a party three years before the trial, and thought that there had been “a confrontation of some sort” between the two men.10 The judge aptly observed that “[t]he simple fact that a juror knew who a defendant was prior to impanelment and had met the defendant briefly at a party three years before (which he may or may not have recalled) does not disqualify him or require him to disclose this fact.” The judge went on to state: “If [the juror] and the defendant were social acquaintances, and particularly, if there was anything unfriendly about their social relationship, the defendant would be the first to bring it forward.”
The judge’s disposition of the defendant’s contention without an evidentiary hearing is supported by Commonwealth v. Amirault, 399 Mass. 617, 625 (1987); Commonwealth v. Dixon, 395 Mass. 149, 151-152 (1985); Commonwealth v. Bianco, 388 Mass. 358, 368, S.C., 390 Mass. 254 (1983); Commonwealth v. Amazeen, 375 Mass. 73, 83 (1978).11
12. There is no reason to excise our authority under G. L. c. 278, § 33E. The defendant received a fair trial, and the jury’s verdict is consistent with the evidence that the defendant acted with malice and a conscious and fixed purpose to kill his wife.
The judgment is affirmed. The order denying the defendant’s motion for postconviction relief is affirmed.
So ordered.