In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 26 scores from all of the students who took the test. She sees that the mean score is 121 with a standard deviation of 14.3688. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 24. Is there evidence that the standard deviation of test scores has decreased at the α=0.05 level? Assume the population is normally distributed.
Step 1 of 5 : H0: σ≥24, Ha: σ<24
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 Determine the value of the test statistic. Round to 3 decimals
Step 4 Reject Null Hypothesis? or Fail to Reject Null Hypothesis?
Step 5 There is sufficient evidence to show that the variance of the share price is different than claimed? or There is not sufficient evidence to show that the variance of the share price is different than claimed?
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