Question about statistics? A teacher gives her a final examination during which he has many years of experience gives an average population of 84 years. Her current class of 24 gets an average of 88 and a standard deviation of 8. Is it correct to assume that the performance of the newer class differs significantly from that of other classes? Using one-tailed test here since the teacher assumed that the class of higher scores.
Null hypothesis:
alternative hypothesis:
Statistical test:
The significance level (I'll get it for you, alpha = .05)
Critical region for rejecting the null hypothesis:
Calculate the statistics (please show your work):
Decision:
H0: <= 84 average
H1: mean> 84
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EDIT: Note that the formal hypotheses are Cidyah mistated as a bilateral test.
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Test - a sample t test to say - a tail
alpha critical value - 0.05, 23 degrees of freedom = 1.714
t = test statistic (88-84) / (8/sqrt (24)) = 4/1.633 = 2.449
Since the test statistic exceeds the critical value, we can reject the null hypothesis in favor of the alternative, and assumes that the latest class different from other classes as a whole.
Null hypothesis: The performance of the latest class does not differ significantly from that of other classes
alternative hypothesis: The score of the class is higher than other classes.
Statistical test: A tail t-test (assuming normality)
The significance level of alpha = .05
Critical region for rejecting the null hypothesis: calculated> t = 1.714 (23 degrees of freedom)
H0: mu = 84
HA: mu not = 84
Average sample 88
The standard deviation = 8
Standard error of mean = SD / sqrt (n)
SE = 8/4.899
Standard error of the mean 1.633
t = (Xbar-mu) / SE
t = (88-84) / 1.633
t = 2.4495
t-statistic = 2.4495
Decision: Calculated t falls in the critical region (greater than 1.714), therefore, reject the null hypothesis. Her class does perform better than other classes.
Posted on July 29, 2010.
