The problem involves a hypothesis test using a normal distribution curve. Let’s address the requested parts based on the image provided:

Part (c): Determine the critical value(s).

The graph indicates that the critical value is a one-tailed test because the rejection region is on the right-hand side of the curve.

From the graph:

• The critical z-value is at $z = 1.812$.

Thus, the critical value is: $z = 1.812$

Part (d): Determine the significance level ($\alpha$).

The graph shows the area of the rejection region shaded in blue, labeled as 0.035. This represents the significance level $\alpha$.

Thus: $\alpha = 0.035$

Would you like further clarification or assistance with constructing the graph or interpreting the results?

Related Questions

1. What is the interpretation of the critical value $z = 1.812$ in this context?
2. How does the significance level $\alpha = 0.035$ influence the likelihood of rejecting $H_0$?
3. Could a two-tailed test be applicable in this scenario? If so, what would the $z$-critical values be?
4. How does the critical value relate to the $p$-value in hypothesis testing?
5. How can this graph be used to visually explain Type I and Type II errors?

Tip

When interpreting hypothesis test results, always compare the test statistic (calculated $z$-value) with the critical value to decide whether to reject or fail to reject the null hypothesis $H_0$.