Question

(Round all intermediate calculations to at least 4 decimal places.) A local botter in Hawaii wishes to ensure that an average of 26 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 43 bottles. The mean weight of the passion fruit juice in the sample is 25 70 ounces Assume that the population standard deviation is 1 19 ounce Use Table 1 Use the critical value approach to test the bottler's concern at a = 0.05. a. Select the null and the alternative hypotheses for the test. Ho u = 26 HA 2+26 Hows 26, HA V > 26 How 2 26; HAN < 26 b-1. Calculate the value of the test statistic (Negative value should be indicated by a minus sign 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? Do not reject Ho since the value of the test statistic is less than the negative critical value Do not reject Ho since the value of the test statistic is not less than the negative critical value Reject Ho since the value of the test statistic is less than the negative critical value Reject Ho since the value of the test statistic is not less than the negative critical value c. (Click to select) Make a recommendation to the bottler. not compromised compromised The accuracy of the bottling process is (Click to select)

Answer 1

The statistic software output for this problem is:

sample Z summary hypothesis test: Mean of population Ho 26 HA u26 Standard deviation 1.19 Hypothesis test results: Mean n Sample Mean Std. Err. P-value Z-Stat 43 25.7 0.1814733 -1.6531358 0.0983

a)

H₀ : μ = 26
H_A : μ ≠ 26

b-1)

Test statistics = -1.65

b-2)

Critical value = $\pm$ 1.65

b-3)

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

c) Compromised