A survey of the wine market has shown that the preferred wine for 17% of Americans is merlot.A wine producer in California where merlot is produced believes the figure is higher in California.She contacts a random sample of 550 California residents and asks which wine they purchase most often.Suppose 115 replied that merlot was the primary wine.Calculate the appropriate test statistic to test the hypotheses.
A)2.25
B)2.44
C)1.11
D)-2.25
E)-2.44

Question

Quizplus · Accepted Answer

We can use the formula for a test statistic for proportions:

z = (p̂ - p) / (√[p(1-p)/n])

Where:

p̂ = proportion in our sample = 115/550 = 0.209
p = hypothesized proportion = 0.17
n = sample size = 550

Plugging in these values, we get:

z = (0.209 - 0.17) / (√[(0.17)(0.83)/550]) = 2.44

Therefore, the appropriate test statistic to test the hypotheses is 2.44, which corresponds to choice B.

A Survey of the Wine Market Has Shown That the Preferred