Question

Consider the test of the claims that the two samples described below come from two populations whose means are equal vs. the alternative that the population means are different. Assume that the samples are independent simple random samples and that both populations are approximately normal with equal variances. Use a significance level of α=0.05 Sample 1: n1=18, x⎯⎯1=28, s1=7 Sample 2: n2=4, x⎯⎯2=30, s2=10

(a) Degrees of freedom =

(b) The test statistic is t =

Answer 1

a)

df = n1 + n2 -2 = 18 + 4 - 2 = 20

b)

Pooled proportion Sp = Sqrt [ (n1-1) S²1 + (n2-1)S²2 / n1 + n2 -2 ]

= Sqrt [ 17 * 7² + 3 * 10² / 20 ]

= 7.5266

Test statistics

t = (1 - 2 ) / [ Sp sqrt ( 1 / n1 + 1 / n2 )]

= (28 - 30) / [ 7.5266 sqrt (1 / 18 + 1 / 4 ) ]

= -0.48

t critical value at 0.05 level with 20 df = 2.086

Since test statistics falls in non-rejection region, do not reject H0.

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