Question 335182
1. state the null hypotheseis (H0) and the alternative hypothesesis (Ha)
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H0: P=0.10
Ha: {{{P<>0.10}}} 
note that this is a two tail test.
P is the population proportion which is unknown
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2. Technically, this is a binomial distribution problem, two outcomes for every student.  Very cumbersome to continue via binomial distribution!
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if you can meet the requirement {{{n*P[0]>10}}} and {{{n*(1-P[0])>10}}} then you can use the Normal approximation to the Binomial

{{{n*P[0]=600*(0.10)=60}}}>10 and {{{n*(1-P[0])=600*(0.90)=540}}}>10, The requirement is met for Normal approximation
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Find the critical value 
{{{type I_error: alpha=0.05}}}, -/+{{{z(0.05/2)}}}=-/+z(0.025)=-/+1.96  (being two tail test the {{{alpha}}} has to be divided by half)
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State the decision rule. 
If Z test statistic < -critical value=-1.96  or Z test statistic > critical value=1.96 then reject Ho
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Compute the value of the Z test statistic. 
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phat=sample proportion=40/600=0.067
test statistic: {{{Z = (phat-P[0])/sqrt(P[0]*(1-P[0])/n)}}} where {{{P[0]}}}=proportion under the null.
Z= (0.067-0.10)/sqrt(0.10*(1-0.10)/600) =-2.69
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Find the p-value
P(Z<=-2.69)+P(Z>=2.69) =0.0036+0.0036=0.0072
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Two ways to make the decision:
1: compare the test statistic vs critical value as stated above
test statistic Z=-2.69 < -critical value=-1.96, thus test falls in the reject region
or
compare the pvalue against the significance level, alpha
since pvalue=0.0072 < {{{alpha=0.05}}} then reject Ho
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conclusion 
The proportion of students at this high school taking diet pills is not 10%