Null hypothesis H0: = $18000. Population mean debt at graduation is equal to $18000.
Alternative hypothesis Ha: < $18000. Population mean debt at graduation is less than $18000.
From the data, Sample mean = 16205.39
Sample standard deviation, SD = 2353.857
Standard error of sample mean, SE = SD / = 2353.857 / = 554.8094
Test statistic, t = ( - ) / SE = (16205.39 - 18000) / 554.8094 = -3.23
Degree of freedom, df = n-1 = 18 - 1 = 17
P-value = P(t < -3.23, df = 17) = 0.0025
Since p-value is less than 0.1 significance level, we reject
null hypothesis H0 and conclude that there is significant evidence
that
population mean debt at graduation is less than $18000.
b)
The required conditions for the statistical test (one-sample t test) in part (a) are -
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