A university claims that their average graduation time for all their students is 4.7 years. The dean of the College of Business and Economics thinks that their students in that college graduate faster. They took a random sample of 150 students from their college and tracked them to see their graduation time. They found that the average graduation time for these students was 4.48 years with standard deviation of 0.83 year. Find the test statistic.
Question
A university claims that their average graduation time for all their students is 4.7 years. The dean of the College of Business and Economics thinks that their students in that college graduate faster. They took a random sample of 150 students from their college and tracked them to see their graduation time. They found that the average graduation time for these students was 4.48 years with standard deviation of 0.83 year. Find the test statistic.
Solution
To find the test statistic, we can use the formula for a one-sample t-test, which is:
t = (X̄ - μ) / (s/√n)
where:
- X̄ is the sample mean
- μ is the population mean
- s is the standard deviation of the sample
- n is the sample size
In this case:
- X̄ = 4.48 (average graduation time for the sample)
- μ = 4.7 (average graduation time claimed by the university)
- s = 0.83 (standard deviation of the sample)
- n = 150 (number of students in the sample)
Substituting these values into the formula, we get:
t = (4.48 - 4.7) / (0.83/√150) = -3.22
So, the test statistic is -3.22.
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