A related-samples t-test has resulted in a and .If the appropriate two-tailed ,construct a 95% confidence interval.

Question

A related-samples t-test has resulted in a  and  .If the appropriate two-tailed  ,construct a 95% confidence interval.

Quizplus · Accepted Answer

The formula for a confidence interval for a related-samples t-test is:

CI = Mdiff ± t(α/2,df) × SE(Mdiff)

where Mdiff is the mean difference between the two samples, t is the t-value from the t-distribution with df degrees of freedom and a significance level of α/2, and SE(Mdiff) is the standard error of the mean difference.

From the problem, we have:

Mdiff = 11eaab01_abbf_ebb7_acdb_f78c428b3c85_TB4035_11 - 11eaab01_abbf_ebb8_acdb_69a4f56b73d5_TB4035_11 = -2.80
Sdiff = 1.77 (given in the problem)
n = the number of pairs of related samples, which is not given in the problem

We cannot determine the exact value of df without knowing the sample size, but we can use the conservative approach of using the smaller of the two sample sizes minus 1. Let's assume an n of 10 (so 10 pairs of related samples).

t(α/2,df) = t(0.025,9) = 2.262 (from a t-table with 9 degrees of freedom and a significance level of 0.025)

SE(Mdiff) = Sdiff / sqrt(n) = 1.77 / sqrt(10) = 0.559

Plugging these values into the formula gives:

CI = -2.80 ± 2.262 × 0.559 = (-4.04, -1.56)

Therefore, the best choice is C because it is the only option that falls within this interval.

A Related-Samples T-Test Has Resulted in a and