Question

The 237 differences in weight (weight after 24 months minus weight before using the wearable technology) are x⎯=−3.5 and =7.8 . Let be the mean weight difference (weight after 24 months minus weight before using the wearable technology).

What is the test statistic ? (Enter your answer rounded to three decimal places.)

Answer 1

The test statistic for the mean weight difference is approximately 5.877.

Step-by-step explanation:

To find the test statistic for the mean weight difference, we need to calculate the standard error of the mean (SEM) and then divide the mean weight difference by the SEM.

The formula for SEM is: SEM = standard deviation / √(sample size)

Here, the mean weight difference, x-bar = (-3.5 + 7.8) / 2 = 2.15; standard deviation = 7.8 - (-3.5) / 2 = 5.65; sample size = 237.

So, SEM = 5.65 / √(237) ≈ 0.365

Now, the test statistic z = mean weight difference / SEM = 2.15 / 0.365 ≈ 5.877

Therefore, the test statistic is approximately 5.877.