A random sample of 81 eighth grade students scores on a national mathematics assessment test has a mean score of 286 with a standard deviation of 32. This test result prompts a state school administrator to declare that the mean score for the states eighth graders on this exam is more than 280. At a=0.04, is there enough evidence to support the administrator claim?
a) Write the claim mathematically and identify Ho and Ha
b) Find the standardized test statistic Z and it corresponding area. If convenient, use technology.
Z = (Round to two decimal places)
Area = (Round to four decimal places)
c) Find the P-Value
P-Value = (Round to four decimal places)
d) Decide whether to reject or fail the null hypothesis
Fail to reject Ho or Reject Ho? (which choice)
e) Interpret your decision in the context of original claim. (which choices)
At the 4% significance level, there (is or is not) enough evidence to (support or reject) the administrators claim that the mean score for the states eighth graders on the exam score is more than 280.
The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.