Question

5) (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.

1. Which set of hypotheses should we use to determine if the mean bottle fill is different from 12 ounces?

A. ?0:?=12 ??. ??:?<12H0:μ=12 vs. HA:μ<12
B. ?0:?=12 ??. ??:?≠12H0:μ=12 vs. HA:μ≠12
C. ?0:?=11.9 ??. ??:?<11.9H0:μ=11.9 vs. HA:μ<11.9
D. ?0:?=12 ??. ??:?>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. Population data must be nearly normal or the sample size must be at least 30.
B. ??̂≥10 ??? ?(1−?̂)≥10np^≥10 and n(1−p^)≥10
C. There must be at least 3 levels of the categorical variable.
D. The observations are independent  
E. There must be an expected count of at least 5 in every cell of the two-way table.

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. little evidence
B. some evidence
C. very strong evidence
D. extremely strong evidence
E. strong evidence
that the null model is not a good fit for our observed data.

Observations Value 12 11.7 12.1 12.1 11.6 11.7 12.2 12 11.9 12 11.7 11.8 12 11.6

Answer 1

Ans:

1)Option B is correct.

?0:?=12 ??. ??:?≠12

2)

Options A and D are correct.

Population data must be nearly normal or the sample size must be at least 30.

The observations are independent  

3)sample mean=11.9

n=16

s=0.189737

Test statistic:

t=(11.9-12)/(0.189737/SQRT(16))

t=-2.1082

4)

degrees of freedom=16-1=15

5)p-value=tdist(2.1082,15,2)=0.0522

6)some evidence