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

a) here null hypothesis: Ho: p<=0.15

alternate hypothesis:Ha: p>0.15

for 0.05 level and right tailed test critical value of z =1.645

Decision rule:reject HO if test statistic z>1.645

std error of proportion =(p(!-p)/n)1/2 =0.0374

sample proportion phat =16/91 =0.1758

tehrefore test statistic z=(phat-p)/std error =(0.1758-0.15)/0.0374 =0.69

as test statsitic is not higher then critical value ; we fail to reeject null hypothesis

we do not have evidence that more then 15% bottles are contaminated.

b)as np =91*0.15 =13.65 and n(1-p)=77.35 both are greater then 10 tehrefore we can use normal approximation of binomial distirbution.

therefore above z test for proportion is appropriate

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