MATH 225N Week 7 Assignment Conducting a Hypothesis Test for Mean - Population

MATH 225N Week 7 Assignment Conducting a HypothesisTest for Mean - Population Standard Deviation Known P-Value ApproachQuestionWhat is the p-value of atwo-tailedone-mean hypothesis test, with a test statistic of z0=−1.73?(Do not round your answer; compute your answer using a value from the table below.)z−1.8−1.7−1.6−1.5−1.4Great work! That's correct.0.084Answer ExplanationCorrect answers:0.084The p-value is the probability of an observed value ofz=1.73or greater in magnitude if the nullhypothesis is true, because this hypothesis test is two-tailed. This means that the p-value could beless than z=−1.73, or greater than z=1.73. This probability is equal to the area under the StandardNormal curve that lies either to the left of z=−1.73, or to the right of z=1.73.A normal curve is over a horizontal axis and is centered on 0. Two points are labeled negative1.73 and 1.72 The area to the right of 1.73 and to the left of negative 1.73 is shaded.Using the Standard Normal Table given, we can see that the p-value that correspondswith z=−1.73 is 0.042, which isjustthe area to the left of z=−1.73. Since the Standard Normalcurve is symmetric, the area to the right of z=1.73 is 0.042 as well. So, the p-value of this two-tailed one-mean hypothesis test is (2)(0.042)=0.084Make a conclusion and interpret the results of a one-mean hypothesis test (populationstandard deviation known) using the P-Value Approach QuestionMary, a javelin thrower, claims that her average throw is 61 meters. During a practice session,Mary has a sample throw mean of 55.5 meters based on 12 throws. At the 1% significance level,does the data provide sufficient evidence to conclude that Mary's mean throw is lessthan 61 meters? Accept or reject the hypothesis given the sample data below.H0:μ=61 meters; Ha:μ<61 metersα=0.01 (significance level)z0=−1.99p=0.0233Great work! That's correct.Reject the null hypothesis because |−1.99|>0.01.Do not reject the null hypothesis because |−1.99|>0.01.Reject the null hypothesis because the p-value 0.0233 is greater than the significancelevel α=0.01.Do not reject the null hypothesis because the value of z is negative.Do not reject the null hypothesis because thep-value0.0233is greater than thesignificance levelα=0.01.Answer ExplanationCorrect answer:Do not reject the null hypothesis because the p-value 0.0233 is greater than thesignificance level α=0.01.In making the decision to reject or not reject H0, if α>p-value, reject H0 because theresults of the sample data are significant. There is sufficient evidence to concludethat H0 is an incorrect belief and that the alternative hypothesis, Ha, may be correct.If α≤p-value, do not reject H0. The results of the sample data are not significant, so thereis not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct.In this case, α=0.01 is less than or equal to p=0.0233, so the decision is to not reject thenull hypothesis.