Question

in a newspapers survey of 468 people, 54.7% 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: 0.5470085
test statistic, z: 2.0339
critical z: ±1.6449
p - value: 0.0420
the null hypothesis is ( h_0: p = 5 ), where p denotes the population proportion of people who say that we should replace passwords with biometric security. reject the null hypothesis.
(type an integer or a decimal. do not round.)
e. what is the final conclusion?
there sufficient evidence to the claim that half of us say that we should replace passwords with biometric security.

Explanation:

Step1: Analyze the P - value

The significance level is \(\alpha = 0.10\). The P - value is \(0.0420\).

Step2: Compare P - value and significance level

Since \(P - value=0.0420<\alpha = 0.10\), we reject the null hypothesis.

Step3: Draw conclusion

When we reject the null hypothesis \(H_0:p = 0.5\), it means there is sufficient evidence to support the claim that the proportion is not \(0.5\). In this case, since the sample proportion \(0.5470085>0.5\) and we reject \(H_0\), there is sufficient evidence to support the claim that the proportion of people who say we should replace passwords with biometric security is not \(0.5\) (in fact, it is greater than \(0.5\) as per the sample result)

Answer:

There is sufficient evidence to support the claim that half of us say that we should replace passwords with biometric security is not True.