Answer
There is not sufficient evidence to support that less than 50% of households have a HD TV.
Work Step by Step
$H_{0}:p=50$%=0.5. $H_{a}:p>0.5.$ $\hat{p}$ is the number of objects with a specified value divided by the sample size. Hence $\hat{p}=0.47.$ The test statistic is:$z=\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}=\frac{0.47-0.5}{\sqrt{0.5(1-0.5)/1500}}=-2.32.$ The P is the probability of the z-score being less than -2.32, hence:P=0.0102. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P=0.0102 is more than $\alpha=0.01$, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to support that less than 50% of households have a HD TV. This result is probably not valid at the moment because more and more people get these TVs nowadays.
