SOLUTION: Hello I need help with my statistic homework I can't understand how this formula works its random sample. the problem is a random sample of 600 high school boys showed 40 had

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Question 335182: Hello I need help with my statistic homework I can't understand how this formula works its random sample. the problem is
a random sample of 600 high school boys showed 40 had taken diet pills during the past 30 days to lose weight the proportion of all high school boys who taken the diet pills to lose weight H0 p=0.10 Ha;p#0.10
1. state the null hypotheseis (H0) and the alternative hypothesesis (Ha)
2. verify necessary data conditions for a z statistic and calculate the z statistic
3. assuming the null hypothesis is true finf the p value ?
4.are the results statistically significant at a significance level of a=0.05 ?what is the conclusion to the context?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
1. state the null hypotheseis (H0) and the alternative hypothesesis (Ha)
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H0: P=0.10
Ha: P%3C%3E0.10
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%2AP%5B0%5D%3E10 and n%2A%281-P%5B0%5D%29%3E10 then you can use the Normal approximation to the Binomial
n%2AP%5B0%5D=600%2A%280.10%29=60>10 and n%2A%281-P%5B0%5D%29=600%2A%280.90%29=540>10, The requirement is met for Normal approximation
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Find the critical value
type+I_error%3A+alpha=0.05, -/+z%280.05%2F2%29=-/+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+=+%28phat-P%5B0%5D%29%2Fsqrt%28P%5B0%5D%2A%281-P%5B0%5D%29%2Fn%29 where P%5B0%5D=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%