2. Natural cork in wine bottles is subject to deterioration, and as a result win

Question

2. Natural cork in wine bottles is subject to deterioration, and as a result wine in such bottles may experience contamination. The article "Effects of Bottle Closure Type on Consumer Perceptions of Wine Quality" (Amer. J. of Enology and Viticulture, 2007: 182-191) reported that, in a tasting of commercial chardonnays, 16 of 91 bottles were considered spoiled to some extent by cork-associated characteristics. Does this data provide strong evidence for concluding that more than 15% of all such bottles are contaminated in this way? A. Carry out a hypothesis test to decide whether more than 15% ofall such bottles are contaminated. Use significance level of 0.05. (Follow the 4-step procedure for full credits.) (8pts) Verify the test you use is appropriate. (2pts) B.

Explanation / Answer

H0: p = 0.15

H1: P > 0.15

p = 16/91 = 0.18

The test statistic Z = (p - P)/sqrt (P * (1 - P)/n)

= (0.18 - 0.15)/sqrt (0.15 * 0.85 /91)

= 0.8

At 0.05 significance level the critical value is 1.96

As the critical value is greater than the test statistic value (1.96 > 0.8), so the null hypothesis is not rejected.

So there is not sufficient evidence at 0.05 significance level that more than 15% of all such bottles are contaminated.

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