A student group maintains that each day, the average student must travel for at
ID: 3128568 • Letter: A
Question
A student group maintains that each day, the average student must travel for at least 25 minutes one way to reach college. The college admissions office obtained a random sample of 26 one-way travel times from students. The sample had a mean of 20.4 minutes and a standard deviation of 9.3 minutes. Does the admissions office have sufficient evidence to reject the students' claim? Use = 0.01.
(ii) Find t. (Give your answer correct to two decimal places.)
(iii) Find the p-value. (Give your answer correct to four decimal places.)
Explanation / Answer
ii)
Formulating the null and alternative hypotheses,
Ho: u >= 25
Ha: u < 25
As we can see, this is a left tailed test.
Thus, getting the critical t,
df = n - 1 = 25
tcrit = - 2.485107175
Getting the test statistic, as
X = sample mean = 20.4
uo = hypothesized mean = 25
n = sample size = 26
s = standard deviation = 9.3
Thus, t = (X - uo) * sqrt(n) / s = -2.522095673 [ANSWER]
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iii)
Also, the p value is
p = 0.009202657 [ANSWER]
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