Problem

Data released by the National Center for Health S…

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Problem 49 Hard Difficulty

On Friday, Wall Street traders were anxiously awaiting the federal government's release of numbers on the January increase in nonfarm payrolls. The early consensus estimate among economists was for a growth of $250,000$ new jobs (CNBC, February $3,2006$ ). However, a sample of 20 economists taken Thursday afternoon provided a sample mean of $266,000$ with a sample standard deviation of $24,000 .$ Financial analysts often call such a sample mean, based on late-breaking news, the whisper number. Treat the "consensus estimate" as the population mean. Conduct a hypothesis test to determine whether the whisper number justifies a conclusion of a statistically significant increase in the consensus estimate of economists. Use $\alpha=.01$ as the level of significance.

Answer

Reject the null hypotheses $H_{0}$

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Essentials of Modern Business Statistics

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Video Transcript

Question 49. We're told that economists were expecting job growth of 250,000 early on in that but that more recently we had a sample of 20 economists whose job expectation growth was averaging 266,000 and the sample standard deviation was 24,000. So we can read some of the stuff down. So initial expectation of job growth with 250,000 has an average. And then we had a sample of 20 economists that were pulled and the sample average. We're expected job growth of those economists was 266,000 and a sample standard deviation of 24,000. And then we were asked, at a significance level of Alfa equals 0.1 to test whether the economists expectations based on the sample for job growth has actually increased. So to do this test, we can make our hypotheses. The no hypothesis is that the mean has not increased so, in other words, that it is less than or equal to 250,000. And the alternative hypothesis does that mean has increased us greater than 250,000 and because we don't have the population standard deviation, and our sample size is not greater than or equal to 30. Our sample averages will be distributed according to the T distribution. So T is there test statistic here and it's equal to the sample average minus the population mean over the sample standard deviation divided by the square root of the sample size, and that comes out to 2.98 So before we go to the tea table, we need to calculate our degrees of freedom and that is able to end minus one. She was 19. So at the tea table of 19 degrees of freedom in our value of 2.98 Paul is between these two values and therefore our Peace Corps is between 0.1 and 0.5 and recall it are significance. Level is Alfa equals 0.1 and it's quite clear that the P value is a lesson Alfa and therefore we can reject the null life offices

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