Question

question 29
0 / 3 points
a training program is tested on 10 employees. the differences in their productivity scores (after - before) are calculated. the mean of these differences is $\bar{x}_d = 5.5$ and the standard deviation of the differences is $s_d = 4.0$. calculate the t - statistic up to two decimal places for a paired t - test to determine if the program was effective. 4.35 × (4.34)

Explanation:

Step1: Recall t - statistic formula for paired t - test

The formula for the t - statistic in a paired t - test is $t=\frac{\bar{x}_d}{s_d/\sqrt{n}}$, where $\bar{x}_d$ is the mean of the differences, $s_d$ is the standard deviation of the differences, and $n$ is the number of pairs.

Step2: Identify the given values

We are given that $\bar{x}_d = 5.5$, $s_d=4.0$, and $n = 10$.

Step3: Substitute values into the formula

$t=\frac{5.5}{4.0/\sqrt{10}}$. First, calculate $\sqrt{10}\approx3.1623$. Then $4.0/\sqrt{10}=\frac{4.0}{3.1623}\approx1.265$. Finally, $t=\frac{5.5}{1.265}\approx4.35$.

Answer:

$4.35$