I'm reading through the statistics chapter in my research methods textbook and think I may have found a mistake. I was hoping someone here could confirm that there's a problem. The mistake deals with using z scores to determine the probability results will fall between two values. Here are the basics of what the book says:
The two z scores are .72 and 1.74. The difference between the two scores is 1.02 or a little over one standard deviation. "We know that 68 percent of the values in an normal distribution lie between one standard deviation below the and one standard deviation above it, that is within a range of two standard deviations. One standard deviation therefore includes 34 percent of the values in a normal distribution, so we can project that approximately 34 percent of our sampled population" falls between the two values.
The two z scores were calculated using two responses from a survey about the number of hours spent on the internet every week. So the question is really dealing with the percentage of the sampled population that might fall between the two responses.
Based on what I've found, it's not as simple as just subtracting one z score from the other. You really need to look at a chart and then subtract the difference between the two values found there. In this case, I think the result should be around 19 percent rather than 34.
Am I missing something here? Is there any way the book could be correct? Thank you in advance for your responses.