A local bottler in Hawaii wishes to ensure that an average of 20 ounces of passi

Question

A local bottler in Hawaii wishes to ensure that an average of 20 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 32 bottles. The mean weight of the passion fruit juice in the sample is 19.63 ounces. Assume that the population standard deviation is 0.80 ounce. Use Table 1. Use the critical value approach to test the bottler's concern at = 0.05. a. Select the null and the alternative hypotheses for the test.

H0: = 20; HA: 20

H0: 20; HA: > 20

H0: 20; HA: < 20

b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.) Test statistic

b-2. Find the critical value(s). (Round your answer to 2 decimal places.) Critical value(s)____ ±____

b-3. What is the conclusion?

Reject H0 since the value of the test statistic is not less than the negative critical value.

Reject H0 since the value of the test statistic is less than the negative critical value.

Do not reject H0 since the value of the test statistic is not less than the negative critical value.

Do not reject H0 since the value of the test statistic is less than the negative critical value.

c. Make a recommendation to the bottler.

The accuracy of the bottling process is: not compromised OR compromised.

Explanation / Answer

Set Up Hypothesis
Null, H0: U=20
Alternate accuracy of the bottling process is compromised H1: U!=20
Test Statistic
Population Mean(U)=20
Given That X(Mean)=19.63
Standard Deviation(S.D)=0.8
Number (n)=32
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=19.63-20/(0.8/Sqrt(32)
Zo =-2.6163
| Zo | =2.6163
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.6163 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -2.6163 ) = 0.0089
Hence Value of P0.05 > 0.0089, Here we Reject Ho

[ANSWERS]
a. H0: = 20; HA: 20
b. Zo =-2.6163
c. Reject H0 since the value of the test statistic is less than the negative critical value
d. The accuracy of the bottling process is compromised

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