Question

You wish to test Ho:μ1=μ2 versus Ha:μ1≠μ2 at α=0.05 You obtain a sample of size n1=8 with a mean of ¯x1=88.4 and a standard deviation of s1=10.3 from the first population. You obtain a sample of size n2=9 with a mean of ¯x2=98.2 and a standard deviation of s2=5.5 from the second population. Assume that the populations are normal with equal variances.

Do not round interim calculations. Round your final answers to three decimal places.

(a). Find the test statistic:  

(b). Using your answer from (a), find the p-value:

(c). Would you fail to reject, accept, or reject the null hypothesis?

Answer 1

a)
Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((8 - 1)*10.3^2 + (9 - 1)*5.5^2)/(8 + 9 - 2))*(1/8 + 1/9))
sp = 3.9369

Test statistic,
t = (x1bar - x2bar)/sp
t = (88.4 - 98.2)/3.9369
t = -2.489

b)
P-value Approach
P-value = 0.025

c)
As P-value < 0.05, reject null hypothesis.