Question 6: (10 marks) With the rapid growth in legalized gambling in US, there

Question

Question 6: (10 marks) With the rapid growth in legalized gambling in US, there is concern that the involvement of youth in gambling activities is also increasing. Professor Stinchfield of the University of Minnesota have done two independent studies. First study was done in 1992 and he reported that 4684 of the 21484 Grade 9 students surveyed gambled weekly. Second study was done in 1998 and he reported that 5313 of the 23199 Grade 9 students surveyed gambled weekly. Do the data provide sufficient evidence indicating that there the proportion of Grade 9 students gambled weekly has increased since 1992?

Explanation / Answer

p1 = 4684/21484 = 0.218

p2 = 5313/23199 = 0.229

H0 : P1 = P2

H1 : P1 < P2

Z critical value = -1.645 at 5% left tailed

ecision rule : if Z statistic > 1.645, then reject H0

Test statistic

= p1 - p2 / p1q1/n1 + p2q2/n2

= 0.218 - 0.229 / 0.218*1-0.218/21484 + 0.229*1-0.229/23199

= -2.79

Here Z statistic < -1.645, reject H0

we conclude that there is sufficient evidence of the proportion of grage 9 students has increased since 1992

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