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 11.7 11.7 11.9 11.9 12.4 12.1 12 11.7 11.9 12.2 11.9 12 12.2 1. Which set of hypotheses should we use to determine if the mean bottle fill is different from 12 ounces? A. H:N = 12 vs. HAH < 12

B. H0:μ=12 vs. HA:μ<12H0:μ=12 vs. HA:μ<12
C. H0:μ=12 vs. HA:μ>12H0:μ=12 vs. HA:μ>12
D. H0:μ=12 vs. HA:μ≠12H0:μ=12 vs. HA:μ≠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. Population data must be nearly normal or the sample size must be at least 30.
D. There must be an expected count of at least 5 in every cell of the two-way table.
E. np^≥10 and n(1−p^)≥10np^≥10 and n(1−p^)≥10

3. Assume the correct conditions have been met and calculate the test statistic.  ? z t X^2 F  =

4. What are the degrees of freedom for this test?

5. Calculate the p-value

6. Based on the p-value, we have:
A. very strong evidence
B. little evidence
C. some evidence
D. strong evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.

Answer 1

The statistical software output for this problem is:

One Sample T hypothesis test: Mean of variable H = 12 H =12 Hypothesis test results: Variable Sample Mean Std. Err. DF T-Stat Data 11.975 0.047871355 15 -0.52223297 P-value 0.6091

Hence,

1. Hypotheses: Option D is correct.

2. Options A and C

3. t = -0.5222

4. DF = 15

5. p - Value = 0.6091

6. Little Evidence