Fresh coffee People of taste are supposed to prefer...

Fresh coffee People of taste are supposed to prefer fresh-brewed coffee to the instant variety. On the other hand, perhaps many coffee drinkers just want their caffeine fix. A skeptic claims that only half of all coffee drinkers prefer fresh-brewed coffee. To test this claim, we ask a random sample of 50 coffee drinkers in a small city to take part in a study. Each person tastes two unmarked cups—one containing instant coffee and one containing fresh-brewed coffee—and says which he or she prefers. We find that 36 of the 50 choose the fresh coffee. (a) We presented the two cups to each coffee drinker in a random order, so that some people tasted the fresh coffee first, while others drank the instant coffee first. Why do you think we did this? (b) Do these results give convincing evidence that coffee drinkers favor fresh-brewed over instant coffee? Carry out a significance test to help answer this question.

Fresh coffee People of taste are supposed to prefer fresh-brewed coffee to the instant variety. On the
other hand, perhaps many coffee drinkers just want their caffeine fix. A skeptic claims that only half of all coffee drinkers prefer fresh-brewed coffee. To test this claim, we ask a random sample of 50 coffee drinkers in a small city to take part in a study. Each person tastes two unmarked cups—one containing instant coffee and one containing fresh-brewed coffee—and says which he or she prefers. We find that 36 of the 50 choose the fresh coffee.
(a) We presented the two cups to each coffee drinker in a random order, so that some people tasted the fresh coffee first, while others drank the instant coffee first. Why do you think we did this?
(b) Do these results give convincing evidence that coffee drinkers favor fresh-brewed over instant
coffee? Carry out a significance test to help answer this question.

Key Concepts

Randomization

Randomization is a key principle in experimental design that involves assigning the order or selection of conditions randomly. This technique helps to eliminate potential biases and confounding variables that might otherwise influence the outcome. By presenting the coffee types in a random order, the study minimizes the risk that the sequence in which the coffees are tasted (such as a potential order effect where the first tasted coffee is more likely to be preferred) could skew the results.

Statistical Hypothesis Testing

Statistical hypothesis testing is a framework used to evaluate an assumption (the null hypothesis) about a population based on sample data. In this context, a null hypothesis could be that only 50% of coffee drinkers prefer fresh-brewed coffee. The process involves calculating a test statistic and determining a p-value, which then informs whether there is sufficient evidence to reject the null hypothesis in favor of an alternative hypothesis.

One-Proportion Test

A one-proportion test is a statistical method used to compare an observed sample proportion to a claimed or known population proportion. It involves determining whether the deviation from the expected proportion is statistically significant. In this example, the test would assess whether the proportion of coffee drinkers who prefer fresh-brewed coffee (observed at 36 out of 50) is significantly different from the hypothesized 50% preference.

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