Question

in a newspapers survey of 491 people, 53.2% 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. use the normal distribution as an approximation to the binomial distribution. use the display and a 0.10 significance level to complete parts (a) through (e)
sample proportion: 0.5315682
test statistic, z: 1.3990
critical z: ±1.6449
p - value: 0.1618
a. is the test two - tailed, left - tailed, or right - tailed?
choose the correct answer below
right - tailed
left - tailed
two - tailed

Explanation:

The claim is that half of us say we should replace passwords with biometric security. The null hypothesis is \(H_0: p = 0.5\) and the alternative hypothesis is \(H_1: p
eq0.5\) (since we are just testing if the proportion is different from 0.5, not specifically greater or less). For a two - tailed test, the critical region is split into two tails. The presence of both positive and negative critical \(z\) values (\(\pm1.6449\)) in the Statdisk display also indicates a two - tailed test.

Answer:

two - tailed