A local bottler in Hawaii wishes to ensure that an average of 25 ounces of passi

Question

A local bottler in Hawaii wishes to ensure that an average of 25 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 66 bottles. The mean weight of the passion fruit juice in the sample is 24.71 ounces. Assume that the population standard deviation is 1.44 ounce.

Use the critical value approach to test the bottler's concern at = 0.01.

1. Select the null and the alternative hypotheses for the test.

A.H0: 25; HA: > 25

B.H0: 25; HA: < 25

C.H0: = 25; HA: 25

2.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.)

3. Find the critical value(s). (Round your answer to 2 decimal places.)

4. What is the conclusion?

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

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

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

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

5. Make a recommendation to the bottler.

The accuracy of the bottling process is (not compromised or compromised).

Explanation / Answer

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   25  
Ha:    u   =/   25   [ANSWER, C]

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2.

Getting the test statistic, as              
              
X = sample mean =    24.71          
uo = hypothesized mean =    25          
n = sample size =    66          
s = standard deviation =    1.44          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.636091068   [ANSWER, TEST STATISTIC]

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3.
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha/2 =    0.005          

Using table/technology,

zcrit = -2.576, 2.756 [ANSWER]

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4.

OPTION B: B.Do not reject H0 since the value of the test statistic is not less than the negative critical value. [ANSWER]

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5.

The accuracy of the bottling process is (not compromised). [ANSWER]

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