Question about TV time I cannot understand:

[smccarthy945]

I have a problem that is basically saying:

In one hour's time in 210 markets, the average times for non programming of tv content are (commercials):

15:48 for prime time
14:55 for cable

Calculating the mean I get 15:22

Part 1 asks: to calculate the difference in the average commercials between network and cable tv. I believe they are asking for the mean?

Part 2 asks: Suppose the standard deviation in the amount of commercials for both the network and cable tv was either 5 minutes or 15 seconds. Which standard deviation would lead you to conclude that there was a major difference in the two commercials averages?

I really don't understand what they are asking for here? Are they just asking to minus out the two times and then add the stat deviation to the mean? I am lost on this one!

[trinker]

Part 1 asks: to calculate the difference in the average commercials between network and cable tv. I believe they are asking for the mean?

No. You're making it too hard on yourself. What does difference mean?

Part 2 asks: Suppose the standard deviation in the amount of commercials for both the network and cable tv was either 5 minutes or 15 seconds. Which standard deviation would lead you to conclude that there was a major difference in the two commercials averages?

This graph will aide our discussion.

When a mean is +/- 2 standard deviations above or below the mean we say the two a significantly different. The standard deviation is the variation of the data away from the mean. So 5 minutes is a greater variation or spread than is 15 seconds. So a graph (bell shaped normal curve in the link I provided) of a 5 minute sd would be a lot wider than the graph of 15 seconds. Now you see how the 2 graphs (normal curves) are on top of each other? The green line represents 2sd's above the mean. 95% of the population falls below this green mark. Now if we have a mean (the high point of the second graph) that is beyond the 2 sd mark (green line) of the first population distribution (first normal curve) we can say there is a significant difference between the two. That means the difference is unlikely to have occurred due to chance because the difference (raw difference between means taking into account the standard deviation (or spread of the people away from the mean) is large enough that we can generalize this to the larger population.

I didn't give you answers but the information to begin thinking through the problem.

[smccarthy945]

Im sorry. I still don't get the basic logic of what the question is asking. This is going over my head.

[trinker]

May I ask your background (including what class this is for) with statistics/math is? This will help me to give you the best answer possible. How I explain this to a high school junior with less math background and a masters student would differ greatly. This is a really important concept (part of the central limit theorem) which is the basis for probability theory, so it's pretty important for you to understand it in order to have a real sense of what those formulas in statistics are really doing (Though I must admit matrix algebra and me are not friends, not yet anyway).

[smccarthy945]

It is an intro to stats class for my MBA courses. I understand all the concepts of mean and stat. dev etc, however, this question is just throwing me off. I think I know what it is asking, however, it just doesn't make sense as to why its not so obvious there is a big difference between 15 seconds and 5 minutes. The question answer is so obvious I don't understand the point of it??

[trinker]

myfile2.pdf
myfile.pdf

I have attached density plots for what your problem would look like as both a 15 sec. standard deviation and a 15 minute standard deviation. For me it's sometimes easier to see things visualy.

So for the one with the a 5 sec the difference between the two plots is very apparent whereas in the plot with the 5minute sd the difference is much less noticable.

NOTE: The mean is roughly around the high point of both graphs

So as the sd decreases it's easier to call a difference between the means

I hope this is helpful.

[Outlier]

Andy Rooney said the benchmark is 15 min of commercials plus 45 min of programming gives you 1 hr.