Final answer:
To determine if teenagers currently spend more than 4.5 hours per week on the phone, a hypothesis test is performed using a sample mean of 4.75 hours and a sample standard deviation of 2.0 from 15 individuals, through the calculation of a t-test statistic and its comparison to t-distribution values.
Step-by-step explanation:
When analyzing whether the mean time that teenagers spend on the phone is higher than a previously reported 4.5 hours per week, a hypothesis test is used. The null hypothesis (H0) is that the mean time is 4.5 hours, while the alternative hypothesis (H1) is that it is greater than 4.5 hours. With a sample mean of 4.75 hours and a sample standard deviation of 2.0 hours from 15 teenagers, we typically use the t-test for a sample size smaller than 30 when the population standard deviation is unknown.
To perform this hypothesis test, we would:
- Calculate the test statistic using the sample mean, known mean (4.5 hours), sample standard deviation, and sample size.
- Compare the test statistic to the t-distribution values to find the p-value.
- Determine if the p-value is less than the chosen significance level (often 0.05), which would indicate whether to reject the null hypothesis.