Question

When conducting a two–tailed test for equality of means, with 𝑛1 = 14, 𝑛2= 26 and 𝛼 =0.05, what is the 𝑡 –critical value when the population variances assumed to be equal?

1. 1.021

2. 1.96

3. 1.645

4. 2.704

5. 2.021

Answer 1

Based on the information provided, the significance level is $\alpha=0.05.$

The degrees of freedom are computed as follows, assuming that the population variances are equal:

$$df=df_1+df_2=14-1+26-1=38$$

Hence, it is found that the critical value for this two-tailed test is $t_c=2.024394$ for

 $\alpha=0.05, df=38.$

5. 2.021