1. The population mean of the random variable $X\textasciitilde{}\text{N}( \mu ,{5}^{2})$ is being tested using a null hypothesis ${\text{H}}_{0}: \mu =20$ against the alternative hypothesis ${\text{H}}_{1}: \mu >20$. A random sample of $n$ observations is taken from the population and the sample mean is calculated as 22.

Using a 10% level of significance, the null hypothesis is rejected. Find the smallest possible value of the sample size $n$.