Question

In the midst of labor negotiations, the CEO of a company argues that the company’s blue-collar workers, who are paid an average of $30,000 a year, are well paid because the mean annual income of all blue-collar workers in the country is less than $30,000. That figure is disputed by the union, which does not believe that the national mean blue-collar income is less than $30,000. An arbitrator draws a random sample of 150 blue-collar workers from across the country and asks each to report his or her annual income. She calculates the sample mean income x = $29,120 and the sample standard deviation s = $8,000. If the population mean annual income of blue-collar workers is less than $30,000 she will order the CEO to make bargaining concessions. a. Test whether the population mean annual income of blue-collar workers is less than $30,000 with a 95% confidence level. The z-critical value for this test is 645 1. z  z0.05  . Show all your steps clearly. b. Explain what is meant by the term “statistically significant”. Is the result you obtained in part a statistically significant?

Answer 1

b)

Statistical significance refers to the claim that a result of data generated by testing or experimentation is not likely to occur randomly or by chance but is instead likely to be attributable to a specific cause.

Statistical significance refers to the claim that a result of data generated by testing or experimentation is likely to be attributable to a specific cause.

If a statistic has high significance then it's considered more reliable.

The calculation of statistical significance is subject to a certain degree of error.

Here we have failed to reject Ho

So we can say that the result is not statistically significant.