Question

newspapers survey of 489 people, 52.1% said that we should replace passwords with biometric security, such as
nts. the accompanying statdisk display results from a test of the claim that half of us say that we should
passwords with biometric security. use the normal distribution as an approximation to the binomial distribution
display and a 0.01 significance level to complete parts (a) through (e).

the proportion: 0.5214724
statistic, z: 0.9497
|z|: ±2.5758
p - value: 0.3423

is the test two - tailed, left - tailed, or right - tailed?
choose the correct answer below.

two - tailed
left - tailed
right - tailed

Explanation:

The claim is that half of us say we should replace passwords with biometric security. In hypothesis testing for a proportion, when the claim is about a specific value (in this case \(p = 0.5\)) without specifying a direction (like \(p>0.5\) or \(p < 0.5\)), it is a two - tailed test. The critical values \(\pm z\) (here \(\pm2.5758\)) also support a two - tailed test as there are two rejection regions (one on the left and one on the right of the distribution).

Answer:

Two - tailed