Researchers at the University of Florida College of Medicine investigated the le

Question

Researchers at the University of Florida College of Medicine investigated the level of caffeine in 16-ounce cups of Starbucks coffee. In one phase of the experiment, cups of Starbucks Breakfast Blend (a mix of Latin American coffees) were purchased on 6 consecutive days from a single specialty coffee shop. The amount of caffeine in each of the six cups (measured in milligrams) is provided below 564 498 259 303 300 307 Suppose the scientists are interested in determining whether the median amount of caffeine in Breakfast Blend coffee exceeds 300 milligrams. Set up the null and alternative hypotheses of interest and give the statistic for the Sign test

Explanation / Answer

following informataion has been generated using ms-excel

null hypothesis H0: Md=300 and

alternate hypothesis H1: Md>300

procedure of sign test

there are one negative and 5 positive sign

so p-value =P(X=1)=0.1875 using binomial distribution with parameter n=6 and p=0.5

The p-value is 0.1875, which is smaller than the alpha level of 0.05.( generally alpha=0.05 is taken)

so we fail to reject H0 and conclude that median is 300

n= 6 median= 305 s= 126.24

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