To solve this hypothesis testing problem, we need to perform a one-sample z-test for proportions. Here's the step-by-step breakdown:

Step 1: Define the hypotheses

• Null Hypothesis (H₀): The accuracy rate for fingerprint identification is equal to 0.8. $H_0: p = 0.8$
• Alternative Hypothesis (H₁): The accuracy rate for fingerprint identification is greater than 0.8. $H_1: p > 0.8$ This is a right-tailed test.

Step 2: Given information

• Sample size (n): You haven't provided the sample size yet, but we can represent it as $n$.
• Number of successes (x): 180
• Significance level ($\alpha$): You haven't specified the significance level yet, but typically it is $0.05$.

For the purposes of this solution, we will calculate the test statistic and p-value assuming $\alpha = 0.05$ and using the general form of the formula.

Step 3: Test statistic formula for proportion

The test statistic for a proportion is calculated using the formula:

$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}$

Where:

• $\hat{p} = \frac{x}{n}$ is the sample proportion of successes.
• $p_0 = 0.8$ is the population proportion under the null hypothesis.
• $n$ is the sample size.

Step 4: Calculate the sample proportion $\hat{p}$

We can calculate the sample proportion $\hat{p}$ as: $\hat{p} = \frac{180}{n}$

Step 5: Calculate the test statistic and p-value

Once you provide the sample size $n$, we can plug in the values into the formula for the test statistic and compute the p-value.

Could you please provide the sample size $n$ so we can proceed with the calculation?