Consider the following computer output: Two-Sample T-Test and CI Difference = mu

Question

Consider the following computer output: Two-Sample T-Test and CI Difference = mu(1) - mu(2) Estimate for difference: -1.210 95% CI for difference (-2.560, 0.140) T-test of difference = 0 (vs not =): T-value = ? P-value = ? DF = ? Both used Pooled StDev = ? (a) Fill in the missing values. Is this a one-sided or a two-sided test? Use lower and upper bounds for the P-value. (b) What are your conclusions if alpha = 0.05 What if alpha = 0.01? (c) This test was done assuming that the two population variances were equal. Does this seem reasonable? (d) Suppose that the hypothesis had been H_0: mu_1 = mu_2 vs. H_0: mu_1

Explanation / Answer

(a)

First calculate the pooled variance, sp2 = (11*1.262 + 15*1.992)/(11+15) = 2.956

Pooled Std Dev, sp = 2.956^0.5 = 1.719

T-value = (-1.210)/(sp*(1/12 + 1/16)0.5) = (-1.210)/(1.719*0.381) = -1.847

DF = 12+16-2 = 26

P-value = 0.0761

This is a two sided t-test.

(b)

alpha a = 0.05

So, for a two sided test,

a/2 = 0.025

Since p>(a/2), so result is not significant.

When a = 0.01, a/2 = 0.005

In this case also, result remains insignificant

(c)

Yes, because the sample sizes don't differ much

(d)

In this case, the t-test will be one sided, and the p-value in this case is 0.038

Here we will compare p with a

Since p < a, so result is significant in this case.

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