Washington’s seasonally adjusted unemployment rate increased to an estimated 9.3 percent in September, up from a revised rate of 9 percent in August, according to the state Employment Security Department.

The estimated rate for August had been reported as 9.2 percent last month, but it was revised downward after more analysis.

The state lost an estimated 16,000 non-agricultural jobs in September, seasonally adjusted, after an estimated loss of nearly 12,000 jobs in August.

K-12 schools were a significant portion of both the August job growth and the September job losses. Employment Security economists attribute the large swings to seasonal-adjustment calculations, which tend to smooth out normal, seasonal changes and amplify unexpected growth or losses.

Industries that lost the most jobs last month were government, which cut 7,100 jobs, mostly in K-12; manufacturing, down 2,700; and construction, which lost 2,300 jobs. Industries that added jobs in September include retail trade, with 300 new jobs; transportation, warehousing and utilities, up 100; and information, up 100.

Year over year, Washington had 131,200 fewer jobs last month than in September 2008, a 4.4 percent decrease.

Nationally, employment declined by 4.2 percent over the past year.

An estimated 312,692 people (not seasonally adjusted) in Washington were unemployed and looking for work in September.

Unemployed workers can inquire about assessment and training opportunities that are available through their local WorkSource career centers.

Employment Security is a partner in the statewide WorkSource system, which offers a variety of employment and training services, including free help with interviewing skills or résumés and with job referrals.

Locations of local WorkSource offices are listed online at www.go2worksource.com. Assistance also is available by phone at 877-872-5627.

In addition, more than 12,800 job openings are posted on www.go2worksource.com.