In order to ensure the consistency of their product, the Oriental Spice Sauce company has a strict policy that the standard deviation of the sodium content in the product is 120mg . For one size of bottle, the sodium content is supposed to be 900mg . In a random sample of 23 bottles, the standard deviation was found to be 183.4773mg . Is there evidence at α=0.025 that the standard deviation of the sodium content exceeds the desired level? Assume the population is normally distributed.
Step 1 of 5:
State the null and alternative hypotheses. Round to four decimal places when necessary.
Step 2 of 5:
Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.
Step 3 of 5:
Determine the value of the test statistic. Round your answer to three decimal places
Step 4 of 5:
Make the decision.
Step 5 of 5:
what is the conclusion?
The statistical software output for this problem is:
Step - 1: Hypotheses:
H0 : σ < 120
HA : σ > 120
Step - 2: Critical value = 36.781
Step - 3: Test statistic = 51.431
Step - 4: Decision: Reject the null
Step - 5: We have sufficient evidence to conclude that the standard deviation of the sodium content exceeds the desired level
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