Question

QUESTION 9 What critical value would I used for the following data? This data will be used to assess a two tailed evaluation with a level of significance of 0.05. The standard deviations (or variances) for the independent populations are not equal. Group A Group B sample mean 5 6 variance.sample 2 9 n 42 58 t critical will be _______________ (to three decimal places)

Answer #1

Given that,

sample mean 1 ( M_{1}) = 5

sample mean 2 (M_{2}) = 6

sample variance 1 = 2

sample variance 2 = 9

sample size ( n_{1}) = 42

sample size ( n_{2}) = 58

The null and alternative hypotheses are,

Since, the standard deviations (or variances) for the independent populations are not equal.

The degrees of freedom is,

t-critical value at significance level = 0.05 with degrees of freedom = 86 is,

Critical value = **1.988**

**Note:** If we take df = min ( n1 - 1, n2- 1)= 41
then critical value is 2.020

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