SOLUTION: A random sample of 600 high school boys showed that 40 had taken diet pills during the past 30 days to lose weight The researcher wants to test the hypotheses below for p = the pro

Question 348176: A random sample of 600 high school boys showed that 40 had taken diet pills during the past 30 days to lose weight The researcher wants to test the hypotheses below for p = the proportion of all high school boys who take diet pills to lose weight.
H0: p = 0.10
Ha: p ≠ 0.10
1.State the null hypothesis (H0) and the alternative hypothesis (Ha) in words.
2.Verify necessary data conditions for a z-statistic and calculate the z-statistic.
3.Assuming the null hypothesis is true, find the p-value.
4.Are the results statistically significant at a significance level of α = 0.05?
5.Report the conclusion in the context of the situation
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A random sample of 600 high school boys showed that 40 had taken diet pills during the past 30 days to lose weight The researcher wants to test the hypotheses below for p = the proportion of all high school boys who take diet pills to lose weight.
H0: p = 0.10
Ha: p ≠ 0.10
1.State the null hypothesis (H0) and the alternative hypothesis (Ha) in words.
Ho: 10% of high school boys take diet pills
Ha: The % of high school boys who take diet pills is not 10%.
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2.Verify necessary data conditions for a z-statistic and calculate the z-statistic.
I'll leave that to you. Check your textbook.
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3.Assuming the null hypothesis is true, find the p-value.
p-hat = 40/600 = 0.4
z(0.4) = (0.4-0.1)/sqrt(0.4*0.6/600) = 15
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p-value = 2*P(z > 15) = 2*3.85x10^-51 = 7.70x10^-71
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4.Are the results statistically significant at a significance level of α = 0.05?
Since the p-value is less than 5%, reject Ho.
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5.Report the conclusion in the context of the situation
The test does not support the claim that the $ of high school
boys taking diet pills is 10%
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cheers,
Stan H.
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