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Forty males and fifty female students at a university were asked to try three brands of soft drinks and select favorite: Their responses are tabulated below: Is the...

Question

Forty males and fifty female students at a university were asked to try three brands of soft drinks and select favorite: Their responses are tabulated below: Is there a relationship between sex of the student and the brand preferred?SexBrandBrand IIBrand IIIMale1219Female2313What is the observed test-statistic?Note: Round answer to two decimal places_Question 51 pt=State your conclusion to the fourth question in one or two sentences

Forty males and fifty female students at a university were asked to try three brands of soft drinks and select favorite: Their responses are tabulated below: Is there a relationship between sex of the student and the brand preferred? Sex Brand Brand II Brand III Male 12 19 Female 23 13 What is the observed test-statistic? Note: Round answer to two decimal places_ Question 5 1 pt= State your conclusion to the fourth question in one or two sentences



Answers

What percentage of your campus student body is female? Let $p$ be the proportion of women students on your campus. (a) If no preliminary study is made to estimate $p,$ how large a sample is needed to be $99 \%$ sure that a point estimate $\hat{p}$ will be within a distance of 0.05 from $p ?$ (b) The Statistical Abstract of the United States, 1 12th edition, indicates that approximately $54 \%$ of college students are female. Answer part (a) using this estimate for $p$.

Oh we want to answer parts A and B of this question per A. States with no point estimate on the population proportion PP hat what sample size N is needed to be 99% sure that the hat will be within 990.5 from the population proportion P. This question is challenging our understanding of how to derive sample size in order to compute a confidence interval or estimate on P that is within a certain error at a certain confidence. So we need to know the correct formula to solve this problem. That formula is and equals 1/4 of the C over E squared where the sea is a critical. The score associated with confidence is the mark of the Earth. For 0.99 we have point to 0.0.58 and for marginal very specified is 0.5 We have N equals 664. That is plugging and Z of 99 E. We obtain and rounding up 664 as our minimum sample size meeting next party. We compute the same thing, but this time we compute it for known P had equals point by four. That is, we have a point estimate on the population portion of periodicals 40.0.5. For this time we're going to use the formula and equals P hat times one minus P hat Z C over E squared again, we use 0.99 E specified as 0.5 And plugging in. This time we obtain, rounding up and equal 662 as a sample size needed.

Okay, So for this problem, we are, ah, hypothetical company or were at least looking at one that is looking at doing a study or a survey. However, you'd like to think about it, Um, testing a new type of fruit drink, which is interesting to think about, I suppose. And we're told that, um, among this group for looking at males and females, which I use an eminent w here respectively, were told that 47% of the group are men. They were then told that from the responses in the surveys, 40% of the males and 54% of the females I said they would drink it. So I used a white here for Yes. So then, with this information, we need to find the probability that if you randomly selected a person So if you just picked a name out of a raffle, what is the probability that they would buy the fruit drink based on the responses? Okay, so I've already drawn out a little diagram, which helps me personally visual eyes and conceptualize what we're looking at. So at the top of the diagram, we have the focus group, which is the biggest, Um, I guess category Because whether your men or a woman or you would or wouldn't buy the drink, you fall under this category. So we have toe break this down into sub categories to see what amount of the bigger group, um, would ultimately by the drink. Because if we're pulling ah name from a raffle or assuming that every single person that is in the focus group could have their name pulled from the raffle. So we need to find what percentage chance they would fall into a subcategory off buying the drink. So we know that there's 40 per seven percent of the people in the group are men, So we need to find out what percentage are woman? Because woman said they would buy the drink in there in the focus groups. Well, so this is pretty easy. You just do a little bit of arithmetic, and they 40% out of 100 our men than the remainder of the 100 have to be woman. So it should be 53%. That's beautiful. So do we need to know the percentage that don't buy it? Not really. Because we're asked the percentage that Dubai it so we could find us out to be relatively easy. Just be 60 because it's again out of we're looking at. How many men said they would or wouldn't buy the drink? 40% said yes. So that means 60% didn't want to buy it out of woman would be 46 based on the same arithmetic there. So now we need to find out out of the 47% you know, that 40% of men said that by the drink. So what percentage is that? Out of the total group. So if we're looking at 47 of 100 originally, you need to see what percentage of that said Yes, right. So let's do 0.47 minus or times 0.4 should be about 0.16 But I will do the math to be extra certain, quite for seven times 0.4 0.188 So it's just round two point 19 So it's 19% out of just the men. So let's do N y for men. Yes, so we'll just anything for the woman. So actually more of the people must study our woman South steer Woman Yes, Out of 100 it's 1000.53 right, because that's a decimal form of 53%. So out of that, subcategory, How many way? See that 54 said yes. So it's 54 off the 53% that are woman. So we do the same thing here. Should be around a little over 2.25 just looking at things quickly, maybe closer to 0.3. But we will do the math to be certain. Okay, so 0.53 times 0.54 is point to 86 Celsius round 20.29 Wonderful. So now, to find what, uh, amounts, that is out of the entire focus group, we just add them up. So if we add these up, this is an eight carry the one and now we have 48 So that's the probability before were 0.48 or percentage form 48% as the probability that selected a random name, they would fall into either the men's yes category or the woman's yes category

To answer this question, we have to focus on each category for each question individually. For the first question, revised papers to improve fighting I mean and female has different reaction to these questions. We see that the first question women have more in just or the often do this. The orphan revised papers toe improve, I think more than men for the second habit. Or for the second question, we can't find the same result that women has this habit more than men. This concludes that women are more interested in mind habits more than me.

In question 14 says the math conference has an attendance of 4950 people, 2110 are college professors. Just put CP and 2575 are female of the college professors 960 or female. So we know that there's 960 female college professors found the probability that air randomly selected Yeah, attendee is female or a college professor. So the probability of female or a college professor. So the probability of female or a college professor in this case would be the probability of female plus the probability of a college professor. And we have to subtract the overlap where that happens at the same time. But we're given all of those things here. Uh, the female would be 25 75 out of 4000, 150. We know that there's 21 10 college professors out of the total, and we know that 960 of those cause professors are female. So we're gonna take that 960 out because they have already been counted, um, in both situations, so they're double counted right now, so the denominator stays the same through the process. We just need to add together the enumerators 25 75 plus 21 10. We're gonna subtract the 9. 60 and we get 37. 25. We can reduce this 21 49 over 1 98. Or we can, Right? This is a decimal, which is point 753 and we can even turn this into a percentage. Approximately 75.3%.


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