In this situation, the random variable is the number or proportion of teens who own a smartphone. You can represent this as a raw number or as a percent of the total population .
The reporters want to know if more than half of the students own a smart phone. So in this case, your null hypothesis is that 50% of teens own a smartphone. In contrast, your alternative hypothesis is what you are looking to prove. In this case, it is that >50% of teens own a smartphone.
If you imagined this as a normal curve, we want to see if more than 50% of our teens have a smart phone, so we will use a one-sided t-test, specifically a right tailed test because we want to see if the percentage is greater than 50%. If we used a left sided t-test, we would be evaluating if it is less than 50%.
Type I errors, or alpha, are when we have false positives. This means we are incorrectly rejecting the null hypothesis. In this case, a Type I error would mean that our data shows that greater than 50% of teens own a smartphone even when in reality 50% or less do.
Type II errors, or Beta, are false negatives, meaning we incorrectly fail to reject the null hypothesis. In this case it would mean that there is not enough evidence to say that more than 50% of teens own a smartphone, when in reality more than 50% do.
