Question

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

Answer 1

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.