To solve this, we will perform a hypothesis test for the population proportion, using the given information to calculate the p-value. Here’s the approach:

1. Define the Hypotheses:

   • Null hypothesis ($H_0$): $p = 0.46$
   • Alternative hypothesis ($H_1$): $p > 0.46$

2. Sample Proportion:

   • Sample size, $n = 227$
   • Number of successes, $x = 114$
   • Sample proportion, $\hat{p} = \frac{x}{n} = \frac{114}{227}$

3. Calculate the Test Statistic: The test statistic for a proportion is calculated as: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}$ where $p_0 = 0.46$.

4. Calculate the p-value: After finding the z-score, the p-value can be found using the standard normal distribution.

Let's perform these calculations.The p-value for this sample is approximately $0.1010$.

Analysis

• Comparison to $\alpha$: The p-value $0.1010$ is slightly greater than $\alpha = 0.10$.
• Decision: Since the p-value is greater than $\alpha$, we fail to reject the null hypothesis.
• Conclusion: There is not sufficient evidence to support the claim that the accuracy rate for fingerprint identification is more than 0.46.

Would you like further clarification or a detailed breakdown of any step?

Related Questions

1. How would the result change if the significance level were 0.05 instead of 0.10?
2. What does failing to reject the null hypothesis imply in the context of fingerprint identification?
3. If the sample size increased while keeping the proportion of successes constant, how would it impact the p-value?
4. How do we interpret a p-value in terms of Type I error in hypothesis testing?
5. Why is it necessary to use a one-tailed test instead of a two-tailed test here?

Tip

Always check whether the test should be one-tailed or two-tailed based on the hypothesis statement, as this affects the interpretation of the p-value and the outcome of the test.