It has been suggusted that the highest priority of retirees is travel. Thus, a study was conducted to investigate the differences in the length of stay of a trip for pre- and post-retirees. A sample of $701$ travelers were asked how long they stayed on a typical trip. The observed results of the study are found below.

Number of Nights	Pre-retirement	Post-retirement	Total
$4-7$	$234$	$175$	$409$
$8-13$	$81$	$68$	$149$
$14-21$	$32$	$52$	$84$
$22$ or more	$22$	$37$	$59$
Total	$369$	$332$	$701$

With this information, construct a table of estimated expected values.

Number of Nights	Pre-retirement	Post-retirement
$4-7$
$8-13$
$14-21$
$22$ or more

Now, with that information, determine whether the length of stay is independent of retirement using $\alpha = 0.01$.

(a) $\chi^2 =$

(b) Find the degrees of freedom:

(c) Find the critical value:

(d) The final conclusion is

A. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alternative hypothesis that the two are dependent.
B. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.