Question

In a certain survey, 511 people chose to respond to this queston: "Should passwords be replaced with biometric securty (frgerprints, etcr Among the respondents, 54% said "yesWe want to test the claim that more then half of the population beleves that passwonds should be replaced with biometic security Complete parts (a) through (d) below a Are any of the three requirements violaled? Can a test about a popuiaton proportion using the normal approximation method be used OA The condtions ro a 5 and nga5 are not satlisfed, so a test about a population proporson using the normal approximation method canot be used OB. The sample observalions are not a random sample, so a test about a population proporion using the normal approximating method cannot be used OC. One of the conditions for a binomial distribution are not satisted, so a best aboud a population proportion uaing the nomal approximating method cannot be used. OD. All of the conditions for tasting a claim about a population proportion using the normal approximation method ane satisfed, so the method can be used b. It was stated hat we can easily remember how to interpret Pvalues with this: f the P is low, the null must go. What does this mean? OA This slaement means thati the Pwalue is very low, the atemative hypothesis should be rejected OB. This statement means that the Pvalue is very low, the null hypothesis should be rejected. OC. This statement means that This stalement means that f the Pvalue is very low, the null hypothesis should be accepted. the Pvalue is not very low, the null hypothesis should be rejected OD

Answer 1

a) In this case, all the three conditions are satisfied:

• np and nq are both greater than 5.
• The sample observations are randomly chosen
• The population does follow Binomial distribution

Hence, we can conduct the Hypothesis testing on the percentage.

b) "If the P-value is low, the null must go" means that if the p-value is significantly low, then we need to reject the null hypothesis.

c) Since the p-value is a means to reject the null hypothesis, getting high p-value does not mean that the null hypothesis is true, it means that there is not enough details to reject the null hypothesis.

d) If we use a significance level with a number like 0.0483, then the probability of rejecting the null hypothesis becomes quite less, thus we almost always will reach at a certain conclusion that the null hypothesis is true. Hence, this significance level will lead us to the desired results only. In fact 1% and 5% significance levels are designed to balance both the probability of rejecting a null hypothesis when it is true and accpeting a null hypothesis when it is false, so that the errors gets reduced.