WASHINGTON — Republicans got their man — and woman — in a half-dozen House primaries as establishment conservatives knocked out right-flank candidates, improving the party’s chances of winning in competitive congressional districts and increasing its majority in November.

With little fanfare, GOP party favorites prevailed in New York, Iowa, New Jersey and Virginia as the outcome in House contests mirrored the headline-grabbing Republican dynamic in the Senate, where incumbents and establishment-backed candidates beat back tea party-supported challenges in the primaries.

House Republicans want to boost their numbers above the current 234-199 advantage, and Arizona poses the next test. of whether the GOP can extend its establishment streak ahead of midterm elections.

In the state’s 1st Congressional District, bigger geographically than the state of Pennsylvania, a bruising, three-way primary pits state House Speaker Andy Tobin against businessman and rancher Gary Kiehne, who had to apologize for saying Democrats pulled the trigger in most of the nation’s mass shootings, and state lawmaker Adam Kwasman, who mistakenly identified YMCA campers as young refugees from Central America.

The winner of the Aug. 26 primary will face Democratic Rep. Ann Kirkpatrick, who won a House seat in 2008, lost it in the 2010 tea party wave and then prevailed by 9,180 votes in 2012. She’s sitting on $1.4 million, far more money that any of the Republicans, and speaks Apache and some Navajo in a district where 24 percent of voters are American Indian.

Tobin, 56, has the backing of the U.S. Chamber of Commerce, Mitt Romney, Barry Goldwater Jr., and plenty of mayors, supervisors and sheriffs. He highlights his record as a businessman as well as his eight-year legislative record, which he says includes cutting taxes, reducing government and improving the Arizona economy.

Of his opponents, he said in an interview, “It’s nice that they’re able to talk a game, but everyone clearly knows that I’m the one who has the record that’s actually accomplished all these things.”

But as of Aug. 14, Tobin had a little more than $82,000 on hand and hadn’t run a television ad, even though early voting began July 31. He declined to say whether he would air a commercial before the primary, insisting his “endorsements alone should send a clear message.”

Tea party-backed Kwasman, 31, is on the air with a commercial that highlights his opposition to the nation’s health care law and Common Core education standards, and boasts of his endorsement from Maricopa County Sheriff Joe Arpaio, the state’s well-known opponent of illegal immigration.

The ad buy was a relatively small $50,000, but Kwasman likes to point to another number — as a state lawmaker he represents 40 percent of a district that is home to the Grand Canyon and Petrified Forest National Park.

He dismisses his rivals for their ties to the establishment and wealth, and maintains he will be his own man in Washington, in the mold of conservatives such as Texas Sen. Ted Cruz and Kentucky Sen. Rand Paul.

“I don’t answer to elephants. I don’t answer to donkeys. I answer to the people,” said Kwasman, who announced a week and a half before the primary that he has a form of slow-growing blood cancer.

Kiehne is airing two ads, one of which says “Washington is broken” and seeks to highlight his status as an outsider, with images of him roping steer. The other spot describes Arizona’s border as “378 miles of crisis,” with Kiehne promising to make border security a top priority.

The blunt-spoken rodeo standout has stirred controversy and been forced to back down for saying, “If you look at all the fiascos that have occurred, 99 percent of them have been by Democrats pulling their guns out and shooting people.”

The GOP is also watching New Hampshire, where former Rep. Frank Guinta is chasing the GOP nomination in the Sept. 9 primary and a possible third rematch with Democratic Rep. Carol Shea-Porter.

In the meantime, the GOP is upbeat about its candidates in New York. State lawmaker Lee Zeldin faces six-term Democratic Rep. Tim Bishop, on the eastern end of Long Island. Along the northern border, 30-year-old Elise Stefanik, who worked in George W. Bush’s administration, hopes to win the seat held by retiring Democratic Rep. Bill Owens.

In a New Jersey district that President Barack Obama won twice, Democrats are high on Aimee Belgard, a member of the Burlington County Board of Freeholders, the county’s governing body, and are spending $1.3 million on ads. Republican Rep. Jon Runyan is retiring after two terms.

Tom MacArthur, a former mayor, secured the GOP nomination over unsuccessful Senate candidate Steve Lonegan, a conservative who has complained about the “the liberal wing of the GOP.”

Republicans dismiss the Democratic optimism, pointing not only to their more moderate candidate but also the commission-driven redistricting changes that moved Democratic-leaning Cherry Hill, New Jersey, out and Republican-leaning Brick Township in.

“It worked out for the whole Republican Party, conservatives, moderates and like-minded people,” said Bill Layton, the Burlington County GOP chairman. MacArthur’s victory is “putting our best foot forward and giving us the best opportunity to win the seat in November.”