Question

concerned 44. A iocal brewery wishes to ensure that an average of 12 ounces of beer is used to fill each bottle. In order to analyze the accuracy of the bottling process, the bottler takes a random sample of 48 bottles. The sample mean weight and the sample standard deviation of the bottles are 11.80 ounces and 0.8 ounce, respectively a. State the null and the alternative hypotheses to test if the accuracy of the bottling process is compromised b. Do you need to make any assumption regarding the population for testing? c. Calculate the value of the test statistic and the p-value. d. At a 0.05, what is the conclusion to the test? Make a recommendation to the bottler.

Answer 1

On average 12 ounce of beer is needed to fill each bottle, that is the population mean ounce needed., Sample size is 48, so z test statistics is used for finding the inference .

n = 48, sample mean = 11.80,

sample standard deviation = 0..8

a). Null Hypothesis : average value = 12 ounce

Alternative value : average value < 12 ounce.

b). No assumption is needed.

c). test statistics and further in image  

Z = -1.733

p value,,, P( Z= -1.733) = 0.0418.

d). Since p-value is less than alphai

0.0418< 0.05 , null hypothesis is rejected.

The bottler need to increase the number of ounce of beer used to fill a bottle as from the samples collected the average ounce used is 11.08 which is less than required 12 ounce,, and is significantly true, as got proved from the test statistics.