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To solve the problem presented, we'll go through each part step-by-step. Let's start with formulating the hypotheses and identifying the type of test.

### Part 1 of 5: State the hypotheses and identify the claim with the correct hypothesis.

The researcher believes that the number of calls made per day today is higher than before cell phones, where the average was 2.7 calls per day.

- Null Hypothesis (\(H_0\)): \(\mu = 2.7\)
- Alternative Hypothesis (\(H_1\)): \(\mu > 2.7\)

This hypothesis test is a **one-tailed (right-tail)** test because the researcher is testing if the mean number of calls is greater than 2.7.

### Part 2 of 5: Find the critical value

Given:
- Significance level (\(\alpha\)): 0.10
- One-tailed test (right-tail)

We need to find the critical value for a right-tailed test at \(\alpha = 0.10\). This corresponds to the z-score where the area to the right is 0.10.

Using z-tables or standard normal distribution, the critical value (\(z_{0.10}\)) is approximately:

\[ z_{0.10} \approx 1.28 \]

### Part 3 of 5: Calculate the test statistic

Given:
- Sample mean (\(\bar{x}\)): 3
- Population mean (\(\mu\)): 2.7
- Population standard deviation (\(\sigma\)): 0.8
- Sample size (n): 33

The formula for the z-test statistic is:

\[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \]

Substituting the values:

\[ z = \frac{3 - 2.7}{\frac{0.8}{\sqrt{33}}} \]
\[ z = \frac{0.3}{\frac{0.8}{5.744}} \]
\[ z = \frac{0.3}{0.1393} \]
\[ z \approx 2.15 \]

### Part 4 of 5: Decision rule

Compare the test statistic to the critical value:

- If \( z \geq 1.28 \), reject \( H_0 \)
- If \( z < 1.28 \), fail to reject \( H_0 \)

Here, \( z = 2.15 \) which is greater than 1.28.

### Part 5 of 5: Conclusion

Since the test statistic (\(z = 2.15\)) is greater than the critical value (\(z_{0.10} = 1.28\)), we reject the null hypothesis.

**Conclusion**: There is enough evidence at the \(\alpha = 0.10\) level to support the researcher's claim that the number of calls made per day today is higher than 2.7.

Would you like more details or have any questions?

Here are 5 questions you might ask:
1. How do you find the critical value using z-tables?
2. What is the importance of the significance level (\(\alpha\)) in hypothesis testing?
3. Can you explain the difference between one-tailed and two-tailed tests?
4. What are the assumptions required for conducting a z-test?
5. How does sample size affect the test statistic?

**Tip:** Always check the assumptions of normality and the population standard deviation before using the z-test.

Learn how to solve a hypothesis testing problem where the researcher tests whether the number of calls made per day today is higher than before cell phones. Includes step-by-step calculations using the z-test statistic formula and interpretation of results.

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