A telephonesurvey gives 501 consumers two choices: Do they prefer Coke orPepsi?

Question

A telephonesurvey gives 501 consumers two choices: Do they prefer Coke orPepsi? Exactly 316 of those surveyed state that they preferCoke. Assuming that â = 0.10, test the hypothesis that the proportion of thepopulation that prefers Coke is 50%.
·        State the null and alternatehypotheses
·        Calculate the sampleproportion
·        Calculate the value of the teststatistic.
·        Determine the criticalvalue(s).
·        State your decision: Should the nullhypothesis be rejected? A telephonesurvey gives 501 consumers two choices: Do they prefer Coke orPepsi? Exactly 316 of those surveyed state that they preferCoke. Assuming that â = 0.10, test the hypothesis that the proportion of thepopulation that prefers Coke is 50%.
·        State the null and alternatehypotheses
·        Calculate the sampleproportion
·        Calculate the value of the teststatistic.
·        Determine the criticalvalue(s).
·        State your decision: Should the nullhypothesis be rejected?

Explanation / Answer

Given n=501, phat=312/501= 0.62 , p=0.5 ·        State the null and alternatehypotheses Ho:p=0.5 Ha:p not equal 0.5 ·        Calculate the sample proportion phat =312/501=0.62 ·        Calculate the value of the teststatistic. Z=(phat-p)/p*(1-p)/n = (0.62-0.5)/sqrt(0.5*(1-0.5)/501) =5.37 ·        Determine the critical value(s). =0.1 , Z(0.05)=1.645 (checknormal table) ·        State your decision: Should the nullhypothesis be rejected? Since Z=5.37 >1.645, we reject Ho.

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