Question

In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Null and Alternative Hypotheses Identify the null hypothesis and alternative hypothesis.

Short answer

The null hypothesis and the alternative hypothesis are as follows:

$H_0:p=0.5$

$H_1:p>0.5$

Here, p represents the proportion of respondents who answered “yes” to the question of “Should Americans replace passwords with biometric security (fingerprints, etc.)?”.

Step-by-step solution

Given information

It is given that out of 510 people who responded to a survey, 53% said “yes” to the question of whether they should replace passwords with biometric security.

Hypotheses

It is claimed that more than half of the population believes that passwords should be replaced with biometric security.

Corresponding to the given claim, the following hypotheses are set up:

Null hypothesis: The proportion of respondents who answered “yes” to the question of “Should Americans replace passwords with biometric security (fingerprints, etc.)?” is equal to 50% or 0.5.

$H_0:p=0.5$

Alternative hypothesis: The proportion of respondents who answered “yes” to the question of “Should Americans replace passwords with biometric security (fingerprints, etc.)?” is greater than 50% or 0.5.

$H_1:p>0.5$