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
p - value = 0.162
(round to three decimal places as needed.)
d. what is the null hypothesis, and what do you conclude about it?
the null hypothesis is ( h_0:p) () (), where ( p) denotes the population proportion of people who say that we should replace passwords with biometric security. () the null hypothesis.
(type an integer or a decimal. do not round.)

Explanation:

Step1: Determine the null hypothesis

The claim is that half of us say we should replace passwords with biometric security. So the null hypothesis \(H_0:p = 0.5\) (since half is \(0.5\) in decimal form).

Step2: Compare the P - value with the significance level

The significance level \(\alpha=0.10\). The P - value is \(0.162\). Since \(P - value=0.162>\alpha = 0.10\), we fail to reject the null hypothesis.

Answer:

The null hypothesis is \(H_0:p = 0.5\). We fail to reject the null hypothesis.