Question

you are conducting a study to see if the accuracy rate for fingerprint identification is significantly different from 0.55. your sample data produce the test statistic . find the p-value accurate to 4 decimal places.

Answer 1

The p-value for the two-tailed test with a test statistic Z = -1.197 is 0.2302. Therefore, there is insufficient evidence to reject the null hypothesis at a significance level of 0.05.

In hypothesis testing, the p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. For a two-tailed test, the p-value is the probability of observing a test statistic as extreme in either tail.

Given Z = -1.197, we look up the corresponding probability in the standard normal distribution table. Since it's a two-tailed test, we find the probability for both tails.

For Z = -1.197, the cumulative probability is approximately 0.1151 in the left tail. Therefore, the probability in the right tail is also 0.1151.

The total p-value is the sum of probabilities in both tails:

`\[ \text{p-value} = 2 * 0.1151 = 0.2302 \]`

So, the p-value accurate to four decimal places is 0.2302.

Que. You are conducting a study to see if the accuracy ratio for fingerprint identification is significantly different from 0.55. Thus, you are performing a two-tailed test. Your sample data produce the test statistic Z = -1.197. Find the p-value accurate to 4 decimal places.

p-value =..............