Executives at Sale Mart Supermarket claim that a typical family of four spends $200 weekly on routine, non-holiday, grocery purchases. According to published industry standards, the population standard deviation is $25.

Stanley, another stats intern at corporate headquarters, wonders if that original claim by the executives is too high. As a project, she collects from store sales receipts a simple random sample (SRS) of size 100. The sample mean for the weekly grocery purchases for a family of four is $197. He is defining as rare, or unusually low, any sample mean that is in the bottom 10% of all possible sample means; hence, he is testing at the 10% level of significance. What conclusion should Stanley draw, based on the available evidence?

What is the critical value, roundedto three decimal places and expressed without insignificant digits?