https://file.aiquickdraw.com/mathbot/file/17299995237186civcjhk.jpg

To determine the correct null and alternative hypotheses for this hypothesis test, let's examine the details provided:

1. **Population Mean (Previous Data):** The organization reported a previous average of 4.5 hours per week.
2. **Research Hypothesis:** The organization thinks that the current mean is higher than 4.5 hours.
3. **Sample Data:** The sample mean is 4.75 hours, and the sample standard deviation is 2.0.

Since we’re testing whether the mean is now higher, this is a **one-tailed test** where we’re only interested in values greater than 4.5 hours. We use the symbol \( \mu \) for the population mean, as it represents the true average hours spent by teenagers.

### Hypotheses
- **Null Hypothesis ( \( H_0 \) ):** The mean time spent on the phone is still 4.5 hours, so \( H_0: \mu = 4.5 \).
- **Alternative Hypothesis ( \( H_a \) ):** The mean time spent on the phone is now greater than 4.5 hours, so \( H_a: \mu > 4.5 \).

### Correct Answer
The correct answer is:
- **\( H_0: \mu = 4.5 \)**
- **\( H_a: \mu > 4.5 \)**

Let me know if you would like more details on hypothesis testing steps or any other questions!

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Here are some follow-up questions related to hypothesis testing:
1. How do you calculate the test statistic for a hypothesis test on the mean?
2. What is the significance level, and how does it affect the hypothesis test?
3. How do we interpret p-values in the context of hypothesis testing?
4. What assumptions must be satisfied for this hypothesis test to be valid?
5. What would a two-tailed test look like for this scenario, and when would it be appropriate?

**Tip:** In hypothesis testing, always determine whether you need a one-tailed or two-tailed test based on the research question.

Previously, an organization reported that teenagers spend 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are:

Conduct a hypothesis test to determine if teenagers currently spend more time on the phone than the previously reported mean of 4.5 hours. Given a sample mean of 4.75 hours and standard deviation of 2.0, this problem explores hypothesis testing with a one-tailed test.

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