Z Tests

$\displaystyle H_0$: there is no difference in the proportion of defective items produced by the two machines.
$\displaystyle H_1$: there is a difference in the proportion of defective items produced by the two machines.

The data is categorical — each item is either defective or not — so the comparison is between two proportions.
A t-test compares means of numerical data, which is not what is being measured here.

$\displaystyle 0.214 > 0.05$, so there is insufficient evidence to reject the null hypothesis.
There is no significant difference in the proportion of adults and teenagers who prefer shopping online. The confidence interval containing zero agrees.

City X: $\displaystyle \frac{312}{500} = 0.624$
City Y: $\displaystyle \frac{245}{550} = 0.445...$, which is $\displaystyle 0.445$ to 3 decimal places.

The p-value is far less than $\displaystyle 0.05$, so reject the null hypothesis.
There is a significant difference in the proportion of households with a smart meter in the two cities.