Test the hypothesis ???? :(?

Question

Test the hypothesis: Ho: u = 60 against the alternative hypothesis H 1: u > 60 at the 5% level of significance given that a SAMPLE MEAN based on a sample of size n = 36 yielded a value of 62.5. The POPULATION standard deviation is known to be 6.2.

Decide whether to accept or reject the null hypothesis. What type of error might you have committed?

Answer 1

ANSWER: "reject the null hypothesis" (Null hypothesis Ho: μ = 60)

"true mean" is greater than 60 to a level of significance 0.05.

"type of error" is TYPE II  (stating contrary as true which "might be false")

SINGLE SAMPLE TEST, ONE-TAILED, 7 - Step Procedure for t Distributions, "one-tailed test"

1. Parameter of interest: "μ" = population mean

2. Null hypothesis Ho: μ = 60

3. Alternative hypothesis Ha: μ > 60

4. Test statistic formula: t = (x-bar - μ)/(s/SQRT(n))

x-bar = estimate of the Population Mean (statistical mean of the sample) [62.5]

n = number of individuals in the sample [36]

s = sample standard deviation [6.2]

μ = Population Mean [60] (used for Test statistic)

5. Computation of Test statistic formula t = (approx) 2.52

6. Determination of the P-value: The test is based on n -1 = 35 df (degrees of freedom). Table "look-up" value shows area under the 35 df curve to the right of t = 2.52 is (approx) 0.008

7. Conclusion: with significance value α = 0.05 the above shows P-value <= α, [0.008 <= 0.05]. Null hypothesis Ho: μ = 60 should be rejected. "true mean" is greater than 60 to a level of significance 0.05.