91Ó°ÊÓ

Given in the question that, the Bureau of Labor Statistics gathers data about employment in the United States. A sample is taken to calculate the number of U.S. citizens working in one of several industry sectors over time. Table 11.17 shows the results:

$\begin{array}{|lllll|}\hline \text{Industry Sector}& \mathbf{2000}& \mathbf{2010}& \mathbf{2020}& \text{Total}\\ \text{Nonagriculture wage and salary}& 13,243& 13,044& 15,018& 41,305\\ \text{Goods-producing, excluding agriculture}& 2,457& 1,771& 1,950& 6,178\\ \text{Services-providing}& 10,786& 11,273& 13,068& 35,127\\ \text{Agriculture, forestry, fishing, and hunting}& 240& 214& 201& 655\\ \text{Nonagriculture self-employed and unpaid family worker}& 931& 894& 972& 2,797\\ \begin{array}{l}\text{Secondary wage and salary jobs in agriculture and private household}\\ \text{industries}\end{array}& 14& 11& 11& 36\\ \text{Secondary jobs as a self-employed or unpaid family worker}& 196& 144& 152& 492\\ Total& 27,867& 27,351& 31,372& 86,590\\ \hline\end{array}$

We want to know if the change in the number of jobs is independent of the change in years. And also need to state the null and alternative hypotheses and the degrees of freedom

Given,

$\begin{array}{|lllll|}\hline \text{Industry Sector}& \mathbf{2000}& \mathbf{2010}& \mathbf{2020}& \text{Total}\\ \text{Nonagriculture wage and salary}& 13,243& 13,044& 15,018& 41,305\\ \text{Goods-producing, excluding agriculture}& 2,457& 1,771& 1,950& 6,178\\ \text{Services-providing}& 10,786& 11,273& 13,068& 35,127\\ \text{Agriculture, forestry, fishing, and hunting}& 240& 214& 201& 655\\ \text{Nonagriculture self-employed and unpaid family worker}& 931& 894& 972& 2,797\\ \begin{array}{l}\text{Secondary wage and salary jobs in agriculture and private household}\\ \text{industries}\end{array}& 14& 11& 11& 36\\ \text{Secondary jobs as a self-employed or unpaid family worker}& 196& 144& 152& 492\\ Total& 27,867& 27,351& 31,372& 86,590\\ \hline\end{array}$

The Bureau of Labor Statistics collects employment data in the United States. The number of Americans employed in one of various industry sectors is calculated throughout time using a sample.

Calculation:

The null hypothesis is as follows:

$H_0$: The number of jobs is unaffected by the number of years.

The alternate hypothesis is as follows:

$H_a$: The quantity of employment available is determined by the years.

The following formula can be used to calculate degrees of freedom:

$df=($number of columns $-1)$$($number of rows $-1)$

$⇒df=(3-1)(7-1)$

$⇒df=2×6$

$⇒df=12$