Is there evidence that the standard deviation has decreased at the α=0.05 level?
A standardized test is given to a sixth-grade class. Historically the mean score has been 151 with a standard deviation of 21. The superintendent believes that the standard deviation of performance may have recently decreased. She randomly sampled 23 students and found a mean of 161 with a standard deviation of 18.2898. Is there evidence that the standard deviation has decreased at the α=0.05 level?
Step 1 of 5 :
State of the hypotheses in terms of the standard deviation. Round the standard deviation 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?
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