Please answer question 10.13. Thank you in advance! 10.12 A random sample of 400 voters in a certain city are asked if theyfavor an additional 4% gasoline sales tax to provide badly neededrevenues for street repairs. If more than 220 but fewer than 260 favor thesales tax, we shall conclude that 60% of the voters are for it.(a) Find the probability of committing a type I error if 60% of thevoters favor the increased tax..(b) What is the probability of committing a type II error using this testprocedure if actually only 48% of the voters are in favor of theadditional gasoline tax?10.13 Suppose, in Exercise 10.12, we conclude that 60% of the votersfavor the gasoline sales tax if more than 214 but fewer than 266 voters inour sample favor it. Show that this new critical region results in a smallervalue for a at the expense of increasing B.

10.13 Given that 60% of the voters favor the gasoline sales tax. There is a sample of 400 voters. That is, n=400 and p=0.60. Acceptance Region: If more than 214 but fewer than 266 voters in our sample favor it. Rejection Region: If less than 214 or greater than 266 voters in our sample does not favor it. Consider, μ=n*p=400*0.60=240σ=np1-p=400*0.6*1-0.6=9.798Alpha: α=PRejecting Null Hypothesis|Null Hypothesis is true =PX<214+PX>266 =PX-μσ<214-μσ+PX-μσ>266-μσ =Pz<214-2409.798+Pz>266-2409.798 =Pz<-2.654+1-Pz≤2.654 =0.0040+1-0.996, by the excel functions, =NORM.DIST(2.654,0,1,TRUE) and =NORM.DIST(-2.654,0,1,TRUE) =0.008 Beta: β=Pfailed rejecting H0|H0 is false Under H1, μ=n*p=400*0.48=192σ=np1-p=400*0.48*1-0.48=9.992 Therefore, β=Pfailed rejecting H0|H0 is false =P214≤X≤266 =P214-1929.992≤X-μσ≤266-1929.992=P2.202≤z≤7.406=Pz≤7.406-Pz≤2.202 =0.014 From the Exercise 10.12, α=0.04β=0.003 From the Exercise 10.13, α=0.008β=0.014 By comparison the α value decreases and the β value increases compared with the results of Exercise 10.12.