Question

In a certain​ survey, 500people chose to respond to this​ question: "Should passwords be replaced with biometric security​ (fingerprints, etc)?" Among the​ respondents,

52​% said​ "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security. Complete parts​ (a) through​ (d) below.

a. Are any of the three requirements​ violated? Can a test about a population proportion using the normal approximation method be​ used?

A.The conditions np≥5 and nq≥5 are not​ satisfied, so a test about a population proportion using the normal approximation method cannot be used.

B. All of the conditions for testing a claim about a population proportion using the normal approximation method are​ satisfied, so the method can be used.

C.The sample observations are not a random​ sample, so a test about a population proportion using the normal approximating method cannot be used.

D. One of the conditions for a binomial distribution are not​ satisfied, so a test about a population proportion using the normal approximating method cannot be used.

b. It was stated that we can easily remember how to interpret​ P-values with​ this: "If the P is​ low, the null must​ go." What does this​ mean?

A.This statement means that if the​ P-value is not very​ low, the null hypothesis should be rejected.

B.This statement means that if the​ P-value is very​ low, the null hypothesis should be rejected.

C.This statement means that if the​ P-value is very​ low, the null hypothesis should be accepted.

D.This statement means that if the​ P-value is very​ low, the alternative hypothesis should be rejected.

c. Another memory trick commonly used is​ this: "If the P is​ high, the null will​ fly." Given that a hypothesis test never results in a conclusion of proving or supporting a null​ hypothesis, how is this memory trick​ misleading?

A.This statement seems to suggest that with a high​ P-value, the alternative hypothesis has been proven or is​ supported, but this conclusion cannot be made.

B.This statement seems to suggest that with a high​ P-value, the null hypothesis has been proven or is​ supported, but this conclusion cannot be made.

C.This statement seems to suggest that with a low​ P-value, the null hypothesis has been proven or is​ supported, but this conclusion cannot be made.

D.This statement seems to suggest that with a high​ P-value, the alternative hypothesis has been​ rejected, but this conclusion cannot be made.

d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like​ 0.0483?

A. A significance level with more than 2 decimal places has no meaning.

B.Choosing a more specific significance level will make it more difficult to reject the null hypothesis.

C. Significance levels must always end in a 1 or a 5.

D.Choosing this specific of a significance level could give the impression that the significance level was chosen specifically to reach a desired conclusion

Answer 1

Here we are conducting a study/Survey of 500 random people "Should Password be replaced by Biometrics"

Out of this 52% d=said yes, andd rest no.

Question a)

Option A) clearly here n =500, p=0.52, so np>5 so option A is not correct

Option B) clearly All the conditions are not met so option B is incorrect

Option C) Here the samples chosen are not randomly selected as IT IS WRITTEN THAT 500 PEOPLE CHOSE O RESPOND so option C is correct

Option D) All conditions for Binomial are mt tht is not a problem so yhis option is incorrect

Question b)

The concept of P value says lower the P value higher becomes the evidence we have to support Alternate hypothesis. Thus leading to reject Null hypothesis in favour of Alternate one only when P value goes below a certain set threshold. Also with a high P value it does not mean that we Accept the null, rather we just conclude that we don't have the evidence from the data to reject null OR we say fail to reject NULL.

BY comparring we could easily see that :

Option B) .This statement means that if the​ P - value is very​ low, the null hypothesis should be rejected.

Question c)

If the P is​ high, the null will​ fly." Given that a hypothesis test never results in a conclusion of proving or supporting a null​ hypothesis, how is this memory trick​ misleading?

By defining the working of How the Pvalue d=should be interpreted as written in Question b)

We get that the correct option is:

Option C) .This statement seems to suggest that with a low​ P-value, the null hypothesis has been proven or is​ supported, but this conclusion cannot be made.

Question d)

Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like​ 0.0483?

this choice of 1% or 5% are more generalized values and can't be altered to favour a certain Outcome.

Option D) .Choosing this specific of a significance level could give the impression that the significance level was chosen specifically to reach a desired conclusion