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Is astrology scientific? The General Social Survey asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education:25(a) Make a bar graph that compares opinions about astrology for the three education categories. Describe what you see.(b) Minitab output for a chi-square test using these data is shown below. Carry out the test. What conclusion do you draw?

a. See histogramb. There is sufficient evidence that there is an association between the variables.

Intro Stats / AP Statistics

Chapter 11

Inference for Distributions of Categorical Data

Section 2

Inference for Relationships

Confidence Intervals

The Chi-Square Distribution

Temple University

Missouri State University

Boston College

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the problem gives the stat about people's opinions on astrology and the groups are Is it scientific or not? And we're breaking it down by their educational degree. Well, the collegiate educational degree from associates, two masters, So not so much. They don't get scientific it all or barely at all. And then, um, at least kind of that, because the way they say this, they say this as, uh, vary, er sort of some calling that kind of basically anyone who's like gonna give it a five out of 10 or up in terms of how scientific it is. So this is the break down. Um, they gave you the data with numbers. What I've done is I've converted that data to proportions because we're going to a bar graph with percentages. So I just went ahead and change these numbers to the percentage of their, uh, respective row So associates not so much is 31% of the people, um, in this row right there. So it's to a bar graph. All right? Her sent. And then what we have, we have, um, pretty have their education, and then there have you. So, percentage wise, we'll get my breakdown up here. It looks like we never go above 50%. So our percent table, we can just do 10 20 30 40 and 50. I don't need to go higher than that. And then we let's go in order. So not scientific, not scientific. I'll be in red education. We can have and associates bachelors and a think masters was last one yet masters. Okay. And then we have 31%. Followed by 48% than 22%. 48% and then 22%. All right. My Mr Graham columns were not perfectly even as usual, but they're good enough to get the point across. You don't even get a little separating lines. So there, that's a little more distinct. Okay, there were into the same thing over here. Associates, bachelors, masters. But for the scientific category. And that's gonna be we got a 44 followed by another 44 followed by a 12. Okay. And then we're supposed to summarize the results. So do we find Well, if you look at this, it looks like to drew Looks like an associates degree. Alright. Should change that. Let's say that a little friendly. An individual with and associates degree was most likely to view astrology as scientific. And when you're doing these rich, always think of the extremes. So if associates was the most extreme, it looks like most adamant against it. Waas the bachelors and masters notice over here that both the bachelors and the masters columns are taller. Then the bachelors and masters over here. So individuals with bachelors or masters, we're most for well, least likely to see astrology as not scientific. All right. And that kind of makes sense. Everything about it. We assume that the more education someone gets, the less likely they are to see astrology is a science. Okay, so that's done. And now we need given that below what you conclude. So we have this chi square test that was given so Oh, no, I French write down, but also wanted us to find to state the hypotheses. I believe the ordinance. We're going down anyway. It's good practice. So normal path says, um, I won't say it's what's the best way to say this? Um, we could say a person's view on the scientific validity of astrology is independent of their education. and then the alternate Apophis would just be that a person's view on the scientific validity. Uh, astrology. It is not independence of their education. And then if we're doing Chi Square, test technically shows, make sure that it meets the necessary conditions. So conditions all right, The conditions that we need to meet our that is random. And the data came from a random sample. We know that they tell us, so that works. Um, the large numbers check. I don't have a written down here, but in the textbook that you would have, it shows you the expected counts and the expected counts are indeed greater than or equal to five. And then let's see, we did that. That Oh, an independent. Um, in this case, we want to think about the fact that the total number of individuals I forgot to calculate the total number. Let me see, you know, quick by three plus okay, it's 6 87 Okay, So the 687 individual individuals in the sample are definitely less than or equal to 10% of the entire population of adults, and so we can treat the probability we can treat the variables as independent, even though, technically we would be sampling without replacement. So all these conditions are met. So now we can talk about the data found the data found. So the p values 0.5 All right, so do Let's do P was less. Well, P is equal 2.5 which is definitely less than 0.5 So we reject no hypothesis. What is that mean? In regular words, it means that we conclude how they say it with our policies. Okay, we conclude a persons have you on astrology to not be independent of there. Education. And it cut me off. Did dio Sorry. Uh, OK, there we go. I can save it. We conclude I lost my train of thought because they kicked me out. We conclude eight persons view of astrology to not the independent of there Oops, education And And we're done

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