Question

Darnell wants to limit his screen time. Last week, he spent an average of 3 1/2 hours on his phone each day. This week, he reduced the amount of time he spent on his phone by ___.

Answer 1

Darnell wants to limit his screen time, but the question does not provide the reduced time. To address the hypothesis test, we first establish the null and alternative hypotheses, then calculate the test statistic using a one-sample t-test, and finally compare the p-value to the significance level to decide whether to reject the null hypothesis.

Step-by-step explanation:

The student's question involves running a hypothesis test to determine if the average time teenagers spend on the phone per week has increased from the previously reported average of 4.5 hours. Since no specific time reduction is mentioned for Darnell's case, we'll focus on the hypothesis test with the provided data of 15 teenagers. The steps to conduct a hypothesis test are:

1. State the null hypothesis (H0) and the alternative hypothesis(Ha). In this case, H0: μ = 4.5 (The mean is 4.5 hours) and Ha: μ > 4.5 (The mean is higher than 4.5 hours).
2. Calculate the test statistic using the sample mean, population mean, sample standard deviation, and sample size.
3. Determine the p-value using the test statistic and decide whether to reject the null hypothesis based on the p-value and the level of significance chosen.

In this scenario, we would calculate the test statistic using the formula for a one-sample t-test because the population standard deviation is unknown and the sample size is less than 30. Assuming the level of significance (alpha) is 0.05, if the calculated p-value is less than 0.05, we would reject the null hypothesis, indicating that the average time teenagers spend on the phone is indeed higher than 4.5 hours.