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The image you've uploaded presents a hypothesis testing problem related to the click-through rate of a website. Based on the context and the provided data, the test is likely testing whether the observed sample proportion of 45% differs significantly from the reported population proportion of 34%.

### Hypothesis setup:
- The null hypothesis (H₀): The population click-through rate is 34% (p = 0.34).
- The alternative hypothesis (H₁): The population click-through rate is not 34%, which would be denoted as p ≠ 0.34.

Given the choices in the image:
- **Correct answer for hypotheses**: H₀: p = 0.34 and H₁: p ≠ 0.34 (Option B).

### Z-test:
You are asked to calculate the z-statistic, which tests the difference between the sample proportion (0.45) and the null hypothesis proportion (0.34). The formula for the z-statistic is:

\[
z = \frac{p_{\text{sample}} - p_{\text{null}}}{\sqrt{\frac{p_{\text{null}} (1 - p_{\text{null}})}{n}}}
\]

Where:
- \( p_{\text{sample}} = 0.45 \)
- \( p_{\text{null}} = 0.34 \)
- \( n = 545 \)

Let's compute the z-statistic.

Do you need me to calculate the z-statistic and p-value for you, or would you like more clarification?

Companies pay large amounts of money to make sure their Web sites are highly ranked on Google. Advanced Web Ranking reported that if your Web site is the very first search result on Google, desktop users will click on that result 34% of the time (this is called a click-through rate). Suppose that a certain company asks its Web manager to report the company's click-through rate. He conducts a random sample of 545 users and reports a click-through rate of 45%. Does this sample give the company reason to believe its results are working better than usual? Or could this just be a lucky result?

Learn about hypothesis testing for proportions using a real-world example of click-through rates. In this case, a sample of 545 users reports a click-through rate of 45%, and we test whether it differs significantly from the claimed 34%. This example covers hypothesis testing concepts like the Z-test, null and alternative hypotheses, and calculation of p-values.

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