A random sample of 25 items from the first population showed a mean of 107 and a

Question

A random sample of 25 items from the first population showed a mean of 107 and a standard deviation of 11. A sample of 17 items for the second population showed a mean of 100 and a standard deviation of 6. Assume the sample populations do not have equal standard deviations.

Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)

The null and alternate hypotheses are:    H0: 1 2 H1: 1 > 2

A random sample of 25 items from the first population showed a mean of 107 and a standard deviation of 11. A sample of 17 items for the second population showed a mean of 100 and a standard deviation of 6. Assume the sample populations do not have equal standard deviations.

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 > 0
(without pooled variances)

Hypothesis test results:

Hence,

a) Degrees of freedom = 38

b) Decision rule: Reject Ho if t > 1.686

c) Test statistic = 2.654

d) Null hypthesis rejected.

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 7 2.6377352 38.531543 2.6537918 0.0058

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