Data from the Motor Vehicle Department indicate that 30% of all licensed divers areolder than age 25.A) In a sample of n = 50 people who recently received speeding tickets, 33 were olderthan 25 years and the other 17 were age 25 or younger. Is the age distribution for thisUse a = .05.sample significantly different from the distribution for the population of licensed drivers?B) In a sample of n = 50 people who recently received parking tickets, 36 were older than25 years and the other 14 were age 25 or younger. Is the age distribution for this samplesignificantly different from the distribution for the population of licensed drivers?Use a = .05. Data from the Motor Vehicle Department indicate that 80% of all licensed drivers are6.older thanA) In a sample of n =than 25 years and the other 17 were age 25 or younger. Is the age distribution for thissample significantly different from the distribution for the population of licensed drivers?age 25.50 people who recently received speeding tickets, 33 were olderUse α- .05.B) In a sample of n = 50 people who recently received parking tickets, 36 were older than25 vears and the other 14 were age 25 or younger. Is the age distribution for this samplesignificantly different from the distribution for the population of licensed drivers?Use a = .05.

Solution: A) Given information: n= 50 Sample size of people x= 33 People were older than 25 years p^=xn=3350= 0.66 Sample proportion of People were older than 25 years p= 0.80 Population proportion of People were older than 25 years. α=0.05 Level of signifcance To test the hypothesis Ho:p=0.80 VS Ha:p≠0.80 Test statistic z=p^-pp×(1-p)nz =0.66-0.800.80×0.2050z =0.66-0.800.1650z =0.66-0.800.0032z=-0.140.056569z= -2.4749 Test statistic z = -2.4749 To find p value p value = 2×P(Z>-2.4749)p value =2×0.006664 From Excel p value = 0.0133 The P value for the test is 0.0133 Decision: P value < α=0.05 Reject the null hypothesis Conclusion: There is sufficient evidence to conclude that the distribution for this sample is significantly different from the distribution for the population licensed drivers. B) Given information: n= 50 Sample size of people x= 36 People were older than 25 years p^=xn=3650= 0.72 Sample proportion of People were older than 25 years p= 0.80 Population proportion of People were older than 25 years. α=0.05 Level of signifcance To test the hypothesis Ho:p=0.80 VS Ha:p≠0.80 Test statistic z=p^-pp×(1-p)nz =0.72-0.800.80×0.2050z =0.72-0.800.1650z =0.72-0.800.0032z=-0.080.056569z= -1.4142 Test statistic z = --1.4142 To find p value p value = 2×P(Z>-1.4142)p value =2×0.078652 From Excel p value = 0.1573 The P value for the test is 0.1573 Decision: P value < α=0.05 Reject the null hypothesis Conclusion: There is insufficient evidence to conclude that the distribution for this sample is significantly different from the distribution for the population licensed drivers.