Community Answer

【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/4Let the sample proportion of 0 to 14 years old be \( \mathrm{\hat{{p}}={0.18}} \)sample size = n = 100.Let the true proportion of 0 to 14 years old be \( \mathrm{{p}={0.1764}} \)significance level \( \mathrm{\alpha={0.05}} \)Hypotheses:\( \mathrm{{H}_{{0}}:{p}={0.1764}} \)\( \mathrm{{H}_{{a}}:{p}\ne{0.1764}} \)This is a two-tail test.Explanation:Please refer to solution in this step.Step2/4Test statistic:\( \mathrm{{z}=\frac{{\hat{{p}}-{p}}}{\sqrt{{\frac{{{p}\times{\left({1}-{p}\right)}}}{{n}}}}}} \)where Z follows the standard normal distribution.\( \mathrm{{z}=\frac{{{0.18}-{0.1764}}}{\sqrt{{\frac{{{0.1764}\times{\left({1}-{0.1764}\right)}}}{{100}}}}}} \)\( \mathrm{{z}=\frac{{{0.0036}}}{\sqrt{{{0.1764}\times{\left({0.8236}\right)}}}}\times{10}} \)\( \mathrm{{z}={0.094}} \)The test statistic is 0.094The p-value:\( \mathrm{{p}-{v}{a}{l}{u}{e}={2}\times{P}{\left({Z}>{0.094}\right)}} \)From excel; The p-value is 0.925109Explanationexcel formula for p-value is:=2*(1-NORM.S.DIST(0.094,TRUE))Explanation:Please refer to solution in this step.Step3/4Decision Rule:Reject the null hypothesis \( \mathrm{{H}_{{0}}} \) if the p-value is less than the significance level \( \mathrm{\alpha} \).Do not reject the null hypothesis \( \mathrm{{H}_{{0}}} \) if the p-value is greater than \( \mathrm{\alpha} \).Conclusion: Since the p-value is greater than \( \mathrm{\alpha} \), hence Do not reject the null hypothesis \( \mathrm{{ ... See the full answer