By Don Lee WASHINGTON -- The number of people filing new jobless claims plunged last week to a 4 1/2-year low. Analysts said the report Thursday probably overstates what appears to be a moderately improving job market. And coming just days after officials reported that the unemployment rate fell in September to a post-recession low, some critics of Obama administration policies may again see political interference in the new data. Thursday's report showed that there were 339,000 initial claims for unemployment benefits in the week ended last Saturday. That's a whopping decline of 30,000 from the prior week. The data are seasonally adjusted, and the claims numbers can be highly volatile from week to week, especially when there is a holiday or the weather is bad and government offices are closed. A Labor Department official economist indicated Thursday that the data could have been skewed by one large state's irregular filing. The steep drop is likely to be met with some skepticism, as was the report last Friday when the government said the jobless rate fell to 7.8 percent last month, from 8.1 percent in August -- the lowest since January 2009, when President Obama was sworn into office. Former General Electric chief Jack Welch triggered a storm of protests after he asserted that the September jobs data were manipulated by the White House. Jobless claims reflect layoffs, which have receded somewhat in recent months even as there's been little evidence of any big movement in hiring. The last time weekly claims were as low as 339,000 was in February 2008, as the economy was beginning what would be a rapid descent. Initial jobless claims rose to a high of 586,000 near the end of 2008, peaking at 667,000 in March 2009. In the past year, initial weekly claims generally have been hovering in the high-300,000 territory. To smooth out the week-to-week volatility, many analysts look at a four-week moving average of new jobless claims. That figure fell by 11,500 to 364,000 for the period ending Oct. 6 - the lowest reading for the measure since May 2008. "Today's 339,000 likely exaggerates the improvement, but its story and the direction of the labor market is real," said Chris Rupkey, chief financial economist at the Bank of Tokyo-Mitsubishi in New York.