Consider the following hypothesis test. H0: 1 - 2 = 0 Ha: 1 - 2 0 The following

Question

Consider the following hypothesis test. H0: 1 - 2 = 0 Ha: 1 - 2 0 The following results are from independent samples taken from two populations. Sample 1 Sample 2 n1 = 35 n2 = 40 x1 = 13.6 x2 = 10.1 s1 = 5.1 s2 = 8.9

a. What is the value of the test statistic (to 2 decimals)?

b. What is the degrees of freedom for the t distribution? (Round down your answer to the whole number)

c. What is the p-value? Use z-table. The area in the upper tail is ; two-tailed p-value is between .

d. At = .05, what is your conclusion? p-value is H0

Explanation / Answer

A) the test statistic is

t = (x1 - x2)/sqrt (s1^2/n1 + s2^2/n2)

= (13.6 - 10.1)/sqrt((5.1)^2/35 + (8.9)^2/40)

= 2.12

B) DF = ((5.1)^2/35 + (8.9)^2/40)^2/(((5.1)^2/35)^2/34 + ((8.9)^2/40)^2/39)

= 63.5 = 64

C) p-value = 2 * P(T > 2.12)

= 2 * (1 - P(T < 2.12))

= 2 * (1 - 0.9811)

= 2 * 0.0189 = 0.0378

D) As the p-value is less than alpha value at alpha = 0.05, so the null hypothesis is rejected.

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