Question

(7 points) A local 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 16 bottles with the following results. The data are shown below. Observations Value 1 11.8 12. 2 3 11.8 4 11.8 5 11.7 6 12 7 11.6 8 12. 9 11.9 10 11.8 11 12.1 12 11.9 13 11.8 14 11.9 15 11.8 16 12 1. Which set of hypotheses should we use to determine if the mean bottle fill is different from 12 ounces?

Answer 1

Solution:

The mean and standard deviation of the given data is:

$\small \bar{x}=11.8813$

$\small s=0.1471$

1. Which set of hypotheses should we use to determine if the mean bottle fill is different from 12 ounces? A. Ho H11.9 vs. HA: < 11.9 B. Ho H12 us. HA 12 C. Ho: 12 us. HA: u< 12 D. Ho u12 us. H: u> 12 2. Which conditions must be met for the hypothesis test to be valid? Check all that apply. A. The observations are independent B. There must be at least 3 levels of the categorical variable. C. There must be an expected count of at least 5 in every cell of the two-way table. D. np 2 10 and n(1 D2 10 E. Population data must be nearly normal or the sample size must be at least 30. 11.8813-12 (?t =-3.23 df n-1 16-1=15 =-3.23 t= 3. Assume the corect conditions have been met and calculate the test statistic. 0.1471 4. What are the degrees of freedom for this test? 15 16 5. Calculate the p-value 0.0056 The excel function is -TDIST(ABS(-3.23), 15, 2) 6. Based on the p-value, we have: A. extremely strong evidence B. strong evidence C. little evidence D. some evidence E. very strong evidence that the null model is not a good fit for our observed data.