Researchers surveyed 600 families in communities where the water isfluoridated a

Question

Researchers surveyed 600 families in communities where the water isfluoridated and found that 69% of them purchased bottled water fortheir families to drink. They researchers surveyed 600 families incommunities where the water was not fluoridated and found that 64%of them purchased bottled water. Assume the families surveyed wereselected randomly.
a) Find a 95% confidence interval for the difference in theproportions of families in communities with and without fluoridatedwater. Interpret your results.
b) The researchers want to determine if families in communitieswith fluoridated water are more likely to buy bottled water thanfamilies that live in communities without fluoridated water. Statethe null hypothesis and alternative hypothesis. Make sure youclearly indicate which parameter is for “withfluoridation” and which is for “withoutfluoridation.”
Ho:
Ha:
c) Calculate the test statistic. Specify which test statistic youare finding (“z” or “t”).
d) Find the p-value using the appropriate table. Draw the curve andhighlight the corresponding area.
e) At a significance level of 0.05, should the null hypothesis berejected or not? Does your conclusion change if the significancelevel is 0.01? Circle the correct answers and explain your choicesby referring to the p-value found in part d.
At = .05 Reject Ho/Do NOT Reject Ho Why?
At = .01 Reject Ho/Do NOT Reject Ho Why?

Explanation / Answer

Let p1:with fluoridation     (p1=0.69)
      p2:without fluoridated (p2=0.64)


(a) Given =0.05, |Z(0.025)|=1.96 (check normal table)

The 95% CI is

(p1-p2) ± Z*[p1*(1-p1)/n1]+[p2*(1-p2)/n2]
--> (0.69-0.64) ± 1.96*sqrt(0.69*(1-0.69)/600 +0.64*(1-0.64)/600)
--> (-0.003, 0.103)

(b)
Ho:p1-p1<=0
Ha:p1-p2>0 (c) The test statistic is
Z=(p1-p2) /[p1*(1-p1)/n1]+[p2*(1-p2)/n2]
=(0.69-0.64) /sqrt(0.69*(1-0.69)/600 + 0.64*(1-0.64)/600)
=1.84 (d) The p-value is P(Z>1.84)=0.0329 (check normaltable)

(e) Since the p-value=0.0329<=0.05, we reject Ho.
     Since the p-value=0.0329>=0.01,we do not reject Ho.

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