Question

Given a result of t (40) = 1.90 for a two-tailed paired samples t-test, answer the following: 10) What is the sample size? 11) What is the tcv? 12) What is the tobt? 13) What should the researcher conclude (accept or reject the null)?

Answer 1

Solution (10)

Given t(40) = 1.90

Degrees of freedom = 40

Let n be the sample size

Degrees of freedom = n - 1

40 = n - 1 => n = 40

Thus, sample size = 41

Solution (11)

As significance value α is not given, we assume it to be 0.05.

The t-critical values for a two-tailed test, for a significance level of α=0.05 and df 40 are

Critical Value t_cv = + 2.021 (Obtained using t distribution table Screenshot attached)

Solution (12)

tobt = 1.90 (Given directly in quesiton)

Solution (13)

Since Critical Value t_cv = + 2.021, the rejection region for the two-tailed test is given by:

t_obt < −2.021 or t_obt > 2.660

In this case, the observed t-value is 1.90 - this is our test statistic. Since t_obt does not fall within the rejection region, we fail to reject H0.

With a test statistic of 1.90 and critical value of ± 2.021 at a 5% level of significance, we do not have enough statistical evidence to reject the null hypothesis. In other words, null hypothesis is accpeted.