Question

Need to find the p-value

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 consen- sus estimate of economists. Use a 01 as the level of significance 49.

Answer 1

Answer

We have to test whether the whisper number justifies a conclusion of a statistically significant increase in the consensus estimate of economists.So, it is a right tailed hypothesis testing because we are testing for an increase.

Null hypothesis:

Alternate hypothesis

Population standard deviation is unknown, so we will use t statistic for testing the hypothesis.

where we have

setting the values, we get

Now, we need to find the corresponding p value

degree of freedom= n-1 = 20-1 = 19

Now, using t distribution table for t value 2.981 with degree of freedom 19, we get

p value= 0.0038

It is clear that p value is less than 0.01 level of significance. So, we can say that our result is significant and we can reject the null hypothesis.

Thus,, we can conclude that there is a significant increase in the consensus estimate of economists.