For a two-sample z-test comparing means from populations with known standard deviations sigma_1 = sigma_2 = 0.8, sample sizes n_1 = 7 and n_2 = 8, the standard error of bar X _1 - bar X _2 is:

Home › MCQs › SSC Statistics › Question #1985

SSC Statistics QUESTION #1985

Question 1

For a two-sample z-test comparing means from populations with known standard deviations \(\sigma_1 = \sigma_2 = 0.8\), sample sizes \(n_1 = 7\) and \(n_2 = 8\), the standard error of \(\bar{X}_1 - \bar{X}_2\) is:

\(\sqrt{\dfrac{0.64}{7} + \dfrac{0.64}{8}}\)✔️
\(\dfrac{0.8}{\sqrt{15}}\)
\(\dfrac{0.64}{7+8}\)
\(0.8\sqrt{\dfrac{1}{7}-\dfrac{1}{8}}\)

Correct Answer Explanation

Since \(\sigma_1 = \sigma_2 = 0.8\), \(SE = \sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}} = \sqrt{\dfrac{0.64}{7}+\dfrac{0.64}{8}} = 0.8\sqrt{\dfrac{1}{7}+\dfrac{1}{8}}\). This is the correct denominator for the z-test statistic.

More Options