A soft drink producing company knew that the proportion of their underfilled bot

Question

A soft drink producing company knew that the proportion of their underfilled bottles was 11%. The old bottle filling production line was replaced by a new one in an attempt to reduce the old proportion of under-filled bottles. A random sample of 120 bottles were selected from the new filling line and it turns out that 12 of them were under-filled. a. Set the appropriate null and alternative hypotheses to test if the proportion of under-filled bottles has decreased. b. What does the TYPE I error mean in the context of tills example. Explain. c. Compute the value of the appropriate test statistic for the hypothesis testing in part (a). d. Compute the p-value for the hypothesis testing problem in part (a) based on the value of the test statistic computed in part (c) and USE the p-value to draw a conclusion at level alpha = 0.05.

Explanation / Answer

a)here paramter of interest is proportion of under filled bottles

here null hypothesis: p>=0.11

alternate hypothesis: p<0.11

b) type I error : rejecting that proportion is 0.11 or greater even if it is true

c) std error =(p(1-p)/n)1/2 =0.0286

phat=12/120=0.1

hence test stat z=(phat-p)/std error =-0.3501

d) for above p value =0.3631

for 0.05 level critical value is z<-1.6449

as test stat z is outside crtical region and p value is greater then 0.05 level we can not reject null hypothesis

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