Question

Using Technology. In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use = 0.05 significance level and answer the following:

a. Is the test two-tailed, left-tailed, or right-tailed?

b. What is the test statistic?

c. What is the P-value?

d. What is the null hypothesis, and what do you conclude about it?

e. What is the final conclusion?

Biometric Security In a USA Today survey of 510 people, 53% said that we should replace passwords with biometric security, such as fingerprints. The accompanying Statdisk display results from a test of the claim that half of us say that we should replace passwords with biometric security.

Short answer

a. The test is two-tailed.

b. The value of the test statistic (z-score) is equal to 1.3284.

c. The p-value is equal to 0.1840.

d. The null hypothesis is that the proportion of people who say that passwords should be replaced with biometric security is equal to 50%.The null hypothesis is failed to reject.

e. There is not enough evidence to conclude that the proportion of people who say that passwords should be replaced with biometric security is not equal to 50%.

Step-by-step solution

Given information

It is given that out of 510 respondents, 53% say that passwords should be replaced with biometric security.

A claim is made that exactly half of the people say that passwords should be replaced with biometric security.

Tail of the test

a.

According to the given claim, the proportion of people who say that passwords should be replaced with biometric security is equal to 50%.

This implies that the alternative hypothesis will be as follows.

Alternative hypothesis: .

As there is a not equal sign in the alternative hypothesis, the test is two-tailed.

Test statistic

b.

The test statistic to test the given claim is the z-score.

Here, the value of the test statistic (z-score) is equal to 1.3284.

P-value

c.

The p-value corresponding to the z-score of 1.3284 is equal to 0.1840.

Null hypothesis and conclusion of the test

d.

The null hypothesis for this test is as follows.

Null hypothesis: The proportion of people who say that passwords should be replaced with biometric security is equal to 50% or 0.5.

Symbolically, $H_0:p=0.5$,where

p is the proportion of people who say that passwords should be replaced with biometric security.

Here, the p-value equal to 0.1840 is greater than the significance level of 0.05. Thus, the null hypothesis is failed to reject.

Conclusion of the test

e.

There is not enough evidence to conclude that the proportion of people who say that passwords should be replaced with biometric security is not equal to 50% or 0.5.