Story highlights Passenger: "The panicked captain said, 'We're in trouble; we're going down'"

Airline says pilot inadvertently activated the PA system

The FAA is investigating

As his plane made a rapid descent to normalize cabin pressure, a Southwest Airlines pilot went on the plane's loudspeaker and apparently told passengers the aircraft was going down.

"At first it sounded like someone was coming over the PA to talk. Then it sounded like shots through the cabin, twice, back to back," passenger Grace Stroud told CNN. "Seconds later, the panicked captain said, 'We're in trouble; we're going down.'"

The flight attendants then began securing the bins, she told "CNN Newsroom" in a separate interview. One told the captain to deploy the oxygen masks.

"I'm sure everybody went through their private moments," Stroud said. "My moment was, 'OK, so this is how I'm going to die,' and 'At least it will be quick.'"

Another passenger, Shelley Wills, told CNN affiliate WTVD that the pilot made the remarks as the plane went into a nosedive when it neared the Raleigh-Durham International Airport.

"He said, 'We're going down.' And everyone is looking around like, 'Is this a joke? Is he serious?' And then you felt the nosedive."

Soon after, the Boeing 737 leveled out and made an emergency landing at the Raleigh airport.

Asked about the WTVD report, a Southwest spokeswoman said it was inaccurate.

"Our pilot said he was descending to 10,000 feet. The report was not accurate from this customer. We landed safely," spokeswoman Whitney Eichinger told CNN.

But in an e-mail the airline sent Stroud, it acknowledged what Stroud suspected may have happened.

"As the captain was communicating his plan with the flight attendants, he inadvertently activated the PA system in the cabin," the e-mail said. "We sincerely regret any confusion caused by the relay of the information."

Southwest Airlines Flight 3426 had taken off from Tampa, Florida, and was headed to Raleigh. As it approached its destination, the pilot noticed a loss of cabin pressure -- prompting him to make a earlier-than-usual descent.

"As the checklist mandates when there is a pressurization issue, our captain did communicate with flight attendants over the PA that he was initiating a descent to a lower altitude," Eichinger said. "The issue resolved itself, which is also not uncommon, and the aircraft landed normally at Raleigh-Durham."

For her part, Stroud said, "I know what I heard."

She said she talked to others seated around her, and they all agreed they heard the pilot say the same thing.

The FAA says it is investigating the incident.

For the "uneasy feelings" the experience may have caused her, Stroud was offered a voucher good toward a future flight.