Question

You calculated the standard deviation of the sample mean differences to be .69. You also calculated the sample mean difference to ge 1.74. Now you'll determine whether the difference is significant

Answer 1

Answer:

Since $|Z| = 2.52 > 2$, the difference is significant.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If |Z| > 2, the measure X is significent.

In this question:

$|X - \mu = 1.74|, \sigma = 0.69$

So

$Z = \frac{1.74}{0.69} = 2.52$

Since $|Z| = 2.52 > 2$, the difference is significant.