A wellness researcher is studying the average daily screen time of adults. In a previous analysis, a random sample of $10$ adults showed a mean daily screen time of $5.38$ hours with a standard deviation of $0.43$ hours. The researcher claims that the population mean daily screen time is $5.2$ hours. Assuming the population of screen times are normally distributed, determine whether the calculated $t$-value falls between $-{𝑡}_{0.05}$ and $t_{0.05}$ at the $90\%$ confidence level.