Hello Diana,

You wish to carry out a hypothesis test involving a population proportion (designated p) at a significance level α = .05. Here, p is the proportion of correctly identified fingerprints. From the alternative hypothesis H_{1}, we note that this is a **one-tail test (to the right.)** The appropriate test statistic is given by

**z = (P - p)/√(pq/n)**,

where

n = sample size

p = population proportion

q = 1 - p

P = sample proportion

[Note that I am using an upper-case p to distinguish the sample proportion from the population proportion.]

To carry out the test, we use the value of the population proportion assumed in the null hypothesis. That is,

p = .87

and thus,

q = 1 - .87 = .13

Note that using these values for p and q (and under the assumption that H_{o} is true), **the distribution of the test statistic is (approximately) equal to the standard normal distribution.**

Also, from the given data, n = 459

and

P = "number of successes"/n = 404/459 ≅ .88017

Now we may calculate the observed value of the test statistic

z = (.88017 - .87)/√(.87·.13/459)

z ≅ .6479

**z ≅ .65**

Next, we determine the p-value. Since the **test is a one-tail test to the right, the p-value is the probability that the test statistic Z is greater than the calculated (observed) value of the test statistic.** That is

**p-value = Prob[Z>.65]**

This is the area under the standard normal distribution to the right of .65. From a table of the standard normal distribution, we find that the area to the left of .65 is .7422, so

p-value = 1 - .7422 =** .2578**

When using the p-value method, **H**_{o}** is rejected if and only if the p-value is less than the significance level α**. In our case, however, the p-value is clearly greater than the significance level of .05. Therefore, **we fail to reject the null hypothesis**. Since we fail to reject H_{o}, this means that we do not have statistically significant evidence in support of H_{1}. Therefore, we can express our final conclusion as:

**D)**** ****There is not sufficient sample evidence to support the claim that the accuracy rate for fingerprint identification is more than 0.87.**

Let me know if you need any further explanation.

William

Diana D.

Thank you william!08/21/19