Question

in a newspapers survey of 489 people, 52.1% 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 0.01 significance level to complete parts (a) through (e).
sample proportion: 0.5214724
test statistic, z: 0.9497
critical z: ±2.5758
p - value: 0.3423
a. is the test two - tailed, left - tailed, or right - tailed?
choose the correct answer below.
two - tailed
left - tailed
right - tailed
b. what is the test statistic?
z = □
(round to two decimal places as needed.)

Explanation:

Step1: Identify the test type

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). A two - tailed test is used when the alternative hypothesis is \(H_1:p
eq p_0\).

Step2: Determine the test statistic

From the Statdisk display, the test statistic \(z\) is given. We just need to round it to two decimal places.

Answer:

a. two - tailed
b. \(z = 0.95\)