1. Calculate the probability of a type ii error for the following hypotheses when µ = 37: ho: µ = 40 h1: µ

1. Calculate the probability of a type ii error for the following hypotheses when µ = 37: ho: µ = 40 h1: µ < 40="" the="" significance="" level="" is="" 5%,="" the="" population="" standard="" deviation="" is="" 5,="" and="" the="" sample="" size="" is="" 25.="" b)="" repeat="" part="" (a)="" with="" a="15%." c)="" describe="" the="" effect="" on="" ß="" of="" decreasing="" a.="" 2.="" surveys="" have="" been="" widely="" used="" by="" politicians="" around="" the="" world="" as="" a="" way="" of="" monitoring="" the="" opinions="" of="" the="" electorate.="" six="" months="" ago,="" a="" survey="" was="" undertaken="" to="" determine="" the="" degree="" of="" support="" for="" a="" national="" party="" leader.="" of="" a="" sample="" of="" 1,100,="" 56%="" indicated="" that="" they="" would="" vote="" for="" this="">


1. Calculate the probability of a type ii error for the following hypotheses when µ = 37: ho: µ = 40 h1: µ < 40="" the="" significance="" level="" is="" 5%,="" the="" population="" standard="" deviation="" is="" 5,="" and="" the="" sample="" size="" is="" 25.="" b)="" repeat="" part="" (a)="" with="" α="15%." c)="" describe="" the="" effect="" on="" β="" of="" decreasing="" α.="" 2.="" surveys="" have="" been="" widely="" used="" by="" politicians="" around="" the="" world="" as="" a="" way="" of="" monitoring="" the="" opinions="" of="" the="" electorate.="" six="" months="" ago,="" a="" survey="" was="" undertaken="" to="" determine="" the="" degree="" of="" support="" for="" a="" national="" party="" leader.="" of="" a="" sample="" of="" 1,100,="" 56%="" indicated="" that="" they="" would="" vote="" for="" this="" politician.="" this="" month,="" another="" survey="" of="" 800="" voters="" revealed="" that="" 46%="" now="" support="" the="" leader.="" a)="" at="" the="" 5%="" significance="" level,="" can="" we="" infer="" that="" the="" national="" leader's="" popularity="" has="" decreased?="" b)="" at="" the="" 5%="" significance="" level,="" can="" we="" infer="" that="" the="" national="" leader's="" popularity="" has="" decreased="" by="" more="" than="" 5%?="" c)="" estimate="" with="" 95%="" confidence="" the="" decrease="" in="" percentage="" support="" between="" now="" and="" 6="" months="" ago.="" 3.="" given="" the="" following="" hypotheses,="" determine="" the="" p-value="" when="" xbar="21," n="25," and="" σ="5." ho="" :="" µ="20" h1="" :="" µ="" ≠="" 20="" b)="" repeat="" part="" (a)="" with="" xbar="22." c)="" repeat="" part="" (a)="" with="" xbar="23." d)="" describe="" what="" happens="" to="" the="" value="" of="" the="" test="" statistic="" and="" its="" p-value="" when="" the="" value="" of="" xbar="" increases.="" 4.="" in="" random="" samples="" of="" 25="" from="" each="" of="" two="" normal="" populations,="" we="" found="" the="" following="" statistics:="" x1="" bar="524" s1="129" x2="" bar="469" s2="131" a)="" estimate="" the="" difference="" between="" the="" two="" population="" means="" with="" 95%="" confidence.="" b)="" repeat="" part="" a)="" increasing="" the="" standard="" deviations="" of="" s="" 1="" to="" 255="" and="" s="" 2="" to="" 260.="" c)="" describe="" what="" happens="" when="" the="" sample="" standard="" deviations="" get="" larger.="" d)="" repeat="" part="" a)="" with="" samples="" of="" size="" 100.="" e)="" discuss="" the="" effects="" of="" increasing="" the="" sample="" size.="" 5.="" ho:="" µ="70" h1:="" µ=""> 70 σ = 20, n = 100, xbar = 80, α = .01 a) calculate the value of the test statistic b) set up the rejection region. c) determine the p-value d) interpret the results