Does Friday's job report really hold the answers?

"Most important jobs report ever" screams the crawl as it slides across the business channel TV screen also filled with flashing red stock quotes that reflect billions of dollars in losses for the day. Indeed, Friday morning's jobs report, which will have the August employment data including the latest jobless rate, is being widely reported as playing a key role in the interest rate decision the Federal Reserve will make at its next meeting Sept. 16 and 17.

The unemployment rate, the statistic that gets the most media play, is the percentage of the workforce that's unemployed and actively looking for a job. It doesn't reflect the millions of workers who have stopped looking.

Conventional wisdom holds that if the Bureau of Labor Statistics reports Friday that the U.S. added at least 200,000 jobs, the economy will still be considered in "recovery" mode and the Fed will be more likely to move ahead with a rate hike, the first in nearly a decade.

The BLS data for August will also include wage trends, hours worked, people working part-time who want full-time jobs and the labor force participation rate (the percentage of Americans with a job or actively looking). It will publish close to 30 different tables to illustrate the dozens of different metrics that make up what it so dryly calls the "employment situation summary."

So, should we be hyper-focused on Friday's jobs report as the way to most accurately judge the relative health of the U.S. economy and the future of interest rates?

"Definitely no," said Jared Bernstein, senior fellow at the Center on Budget and Policy Priorities. "I am frankly concerned that so much reliance is being put on such a noisy indicator that reflects just one month."

Bernstein, who has served as a top economic advisor in the Obama administration, warned that taken alone, the jobless rate can be deceiving. "When the unemployment rate falls, it's not necessarily good news," he said. "It could mean you had more jobs created, but it could also mean more people dropped out of the labor market."

For Bernstein, the more relevant data points are indicators like wage growth. "If a labor market is truly nearing full employment, we should see more in the way of wage growth, something we have seen in the past."

"The jobs report leaves out the all-important issue of people 'leaving the labor force' -- a number in the millions since the Great Recession began in 2007," said Richard Wolff, an economist and visiting professor at the graduate program in international affairs at the New School University. "Those millions voted with their feet in disgust over the quality as well as quantity of jobs available."

For Cato Institute senior fellow Alan Reynolds, the Fed's fixation on the unemployment rate springs from what he thinks is an errant notion that there's a link between the status of the labor market and controlling the rate of inflation, the other factor the Fed has a mandate to monitor.

"A lot of countries have high inflation and have high unemployment," said Reynolds. "Look at Venezuela." Reynolds agreed with Wolff, saying the more obscure labor force participation rate "is a more critical number, which has been extremely depressed for six years."

As of the last jobs report, the labor force participation rate, which has been declining for decades, was at 62.6 percent, a level not seen since the 1970s. "If the economy were really strong," Reynolds told CBS MoneyWatch, "you would see these dropouts coming back."