A rent$-$to$-$own $($RTO$)$ agreement allows immediate access to merchandise, and by making all payments, the consumer acquires the merchandise. At the same time, goods can be returned at any point without penalty. Suppose a recent study documents that $65\%$ of RTO contracts are returned, $30\%$ are purchased, and the remaining $5\%$ default. In order to test the validity of this study, an RTO researcher looks at the transaction data of $470$ RTO contracts, of which $313$ are returned, $124$ are purchased, and the rest defaulted.

b$.$ Compute the value of the test statistic.

Note: Round the intermediate calculations to at least $4$ decimal places and final answer to $3$ decimal places.