Question

50 random teenagers were asked how many hours a day they use their phone. They spent an average of 7 hours a day with a standard deviation of 1.3. Based on the results, what is the margin of error for the true mean number of hours a teenager spends on their phone?your margin of error on a 95% confidence level, round your answer to the nearest tenth

Answer 1

Answer:

The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.

Step-by-step explanation:

We have the standard deviation of the saple, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 50 - 1 = 49

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$. So we have T = 2

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2\frac{1.3}{\sqrt{50}} = 0.4$

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.