Question

# A provost thinks that the mean age of students at his college is not 21.2, like...

A provost thinks that the mean age of students at his college is not 21.2, like it was last school year. In a random sample of 18 students, the mean age was 22.5 and the standard deviation was 1.3. Test the provost’s claim. Use α = 0.10. a 1-6) Give the hypotheses for H0 (a1, a2 and a3) and H1 (a4, a5 and a6) H0 a1) µ or p a2) =, ≥, ≤ a3) Number H1 a4) µ or p a5) ≠, >, < a6) Number b) Calculate the test statistic. t = _____ (Round your answer to 3 decimals.) Number c 1-3) Formulate the decision rule for the critical value approach. Reject H0 if (c1 c2 c3) c1) |t| or |p| c2) > or < c3) Number d 1) Make a decision(d1). d1) reject Ho or do not reject Ho e1-2) Give your conclusion. At α = .___, there (is/is not) enough evidence to conclude that the mean age of students at his college is not 21.2, like it was last school year. e1) Number e2) is or is not

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 21.2
Alternative Hypothesis, Ha: μ ≠ 21.2

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (22.5 - 21.2)/(1.3/sqrt(18))
t = 4.243

c)

Rejection Region
This is two tailed test, for α = 0.1 and df = 17
Critical value of t are -1.74 and 1.74.
Hence reject H0 if t < -1.74 or t > 1.74

d)

reject Ho

e)

At α = 0.1, there (is) enough evidence to conclude that the mean age of students at his college is not 21.2, like it was last school year.

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