To test if the variance of population 2 is higher than the variance of population 1 at a 10% level of significance, we can use the F-test for equality of variances.

The null hypothesis is that the variances are equal: H0: 1^2 = 2^2 The alternative hypothesis is that the variance of population 2 is higher than the variance of population 1: Ha: 1^2 < 2^2 (one-tailed test)

The test statistic is the F-statistic:

F = s2,2^2 / s1,1^2

where s1,1^2 and s2,2^2 are the sample variances for sample 1 and sample 2, respectively.

The critical value for the F-test at a 10% level of significance with 15 degrees of freedom for the numerator and 10 degrees of freedom for the denominator is 2.727.

Calculating the test statistic:

F = s2,2^2 / s1,1^2 = 5^2 / 4.5^2 = 1.23

Since 1.23 < 2.727, we fail to reject the null hypothesis. There is not enough evidence to conclude that the variance of population 2 is higher than the variance of population 1 at a 10% level of significance.