Test the hypothesis ?

Question

Test the hypothesis H o: u = 60 aginst an alternative hypothesis H 1: u > 60 at the 5% level of significance given that a sample of size n = 36 yielded a sample mean of 62.8 and the population standard deviation is known to be 7.

Answer 1

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

Why???

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) [62.8]

n = number of individuals in the sample [36]

s = sample standard deviation [7]

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

5. Computation of Test statistic formula t = 2.4

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 = 2.4 is (approx) 0.011

7. Conclusion: with significance value α = 0.05 the above shows P-value <= α, [0.011 <= 0.05]. Null hypothesis Ho: μ = 60 should be rejected. "true mean" is greater than 60 to a level of significance 0.05.