One way developers continue to make money off their consumers for free$-$to$-$play games is through in$-$game purchases such as character skins, emotes, accessories, etc. One study claimed that, on average, players spend around $$205$ a year on in$-$game purchases.

To determine if this is true, a random sample of $41$ consumers showed that in a year they spent a sample mean

x

$=$ $$210$ with sample standard deviation s $=$ $$13\mathrm{.}69.$ Use a $5\%$ level of significance to test the claim that the yearly mean spending by consumers on in$-$game purchases is greater than $$205.$

Compute the appropriate sampling distribution value of the sample test statistic. $($Round your answer to two decimal places.$)$