Arandom sample of 78 eighth grade students' scores on a national mathematics assessment test has a mean score of 284. this test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 275. assume that the population standard deviation is 32. at α=0.04, is there enough evidence to support the administrator's claim a) h0: μ≤275 ha: μ> 275(claim) b) find the standarized test statistic z and its corresponding area c) find the p value d) describe whether to reject or fail the null hypothesis e) interpret your decision in the context of the original claim

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?