A candy enthusiast is concerned that the manufacturer of her favorite candy is not including as much candy is advertised on the packaging. The manufacturer claims that there is a pound of candies in each bag (16 oz). The enthusiast decides to buy 10 bags of candy and will take their average weight. If the average weight is less than 15 oz, she will decide that the manufacturer is guilty of false advertising.

What is the question?

In plain language, establish an appropriate null hypothesis for this situation. What should be the associated alternative hypothesis?

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• Null Hypothesis: The manufacturer is telling the truth and the true average weight of candy per bag is 16 oz.
• Alternative Hypothesis: The manufacturer is exaggerating and the true average weight of candy per bag is less than 15 oz. </aside>

Establish mathematical notation

Parameter of interest: $p$, the true proportion of eventual voters who support Candidate A.

Let $\hat{p}$ represent the proportion of individuals in the survey who say they support Candidate A.

Let $n$ represent the number of individuals who participate in the survey.

Let $X$ represent the number of individuals in the survey who say they support Candidate A.

Question: Articulate this investigation as a hypothesis test assuming that the null hypothesis ca be stated as “The candidates are currently tied.”

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Hypothesis Test

• Null Hypothesis: $H_0: p = 0.5$
• Alternative Hypothesis: $H_A: p < 0.5$
• Test Statistic: $TS: \hat{p} = X/n$
• Rejection Criterion: $\hat p < 0.48$ or $\hat p > 0.52$. </aside>

Question: Suppose that 500 individuals are surveyed and 225 say they support Candidate A. Determine the values $n$, $X$, and $\hat{p}$ and choose the appropriate conclusion.

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Multiple Choice

1. There is sufficient evidence to reject the null hypothesis. Candidate A is winning the race.
2. There is sufficient evidence to reject the null hypothesis. Candidate B is winning the race.
3. There is not sufficient evidence to reject the null hypothesis. Neither candidate has a substantial lead. </aside>

Solution: $n = 500$ and $X = 225$, so $\hat{p} = 0.45.$ This experimental outcome meets the rejection criterion, so we can reject the null hypothesis that the candidates are tied. Since $0.45 < 0.5$, we conclude that Candidate B is winning, so the best choice is (b).