P. 3 An agency published the data that 75% of the adult population are in favor
ID: 3052862 • Letter: P
Question
P. 3 An agency published the data that 75% of the adult population are in favor of tougher legis- lation for antipollution measures. A journalist believes that this data is not accurate. From telephone interviews with 15 adults, he found that 12 of them supported tougher legislation for antipollution measures (a) What is the range of the number of supporters in the 15 interviewee that would substan- tiate the journalist's belief on 8% significance level? (b) Does the above poll substantiate the journalist's belief on 8% significance level? (c) Find the p-value and formulate the decision using the p-valueExplanation / Answer
Ans:
a)sample proportion=12/15=0.8
92% confidence interval for p
=0.8+/-1.75*sqrt(0.8*(1-0.8)/15)
=0.8+/-0.18
=(0.62,0.98)
in terms of number of supporters 0.62*15=9.3 to 0.98*15=14.7
i.e it wil be 9 to 15 supporters.
b)As,75% is included within confidence interval limits(0.62, 0.98),so it is substantial.
c)
z=(0.8-0.75)/sqrt(0.75*0.25/15)
z=0.45
p-value(2 tailed)=0.6547
As,p-value>0.08,teh above data supports the jornalist belief.
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