A principal claims the students in his school have above-average test scores for a particular standardized test.
A sample of 50 students from his school were found to have an average test score of 77.2.
The population mean for test scores for this particular test is 75, with a standard deviation of 9 (so we can assume that the population test score is normally distributed).
Set up a hypothesis test to determine whether this principal’s claim is correct (use alpha of 0.05), and determine what constitutes a Type I error and Type II error in this case.
H0:Null Hypothesis: 75
HA: Alternative Hypothesis: 75
SE = /
= 9/ =1.2728
Test statistic is:
Z = (77.2 - 75)/1.2728 =1.73
One Tail - Right Side Test
From Table, critical value of Z = 1.645
Since calculated value of Z = 1.73 is greater than critical value of Z = 1.645, the difference is significant. Reject null hypothesis.
The data support the claim that the students in his school have above average test scores fora particular standardized test.
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