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Although 85% of the general public is right-handed, a survey of300 chief executive officers of large corporations found that 96were right-handed.a) Is this differen...

Question

Although 85% of the general public is right-handed, a survey of300 chief executive officers of large corporations found that 96were right-handed.a) Is this difference in percentages statistically significant?Test using α = 0.01.b) Find (approximate) the p-value for the test and explain whatit means.

Although 85% of the general public is right-handed, a survey of 300 chief executive officers of large corporations found that 96 were right-handed. a) Is this difference in percentages statistically significant? Test using α = 0.01. b) Find (approximate) the p-value for the test and explain what it means.



Answers

Lefties Refer to Exercise 1. In Simon’s SRS, 16 of the students were left-handed. A significance test yields a P-value of 0.2184.
(a) Interpret this result in context.
(b) Do the data provide convincing evidence against the null hypothesis? Explain.

In question 11, it says, refer to exercise one. In Simon's simple random sample, 16 of the students were left handed. A significance test yields a P value of 0.2184 So let's look back at question one. Simon reads a newspaper report claiming that 12% of all adults in the United States or left handed he wonders if the 12% of the students at his large public high school are left handed. So he chooses a simple an example of 100 students and records whether each student is right left handed. So he says that 16 of these 100 students were left handed, and it says a significance test yields a P value of 0.2184 are a interpret the result in contact, so we want to interpret the P value of 0.2184 So, in this case, if the true proportion of lefties at Simon School really is 0.12 which is the national proportion, there is a 21.84% chance of finding a sample of 100 people with the value as far or further from 1000.12 than the Value and Simon sample in Part B, it says, Do the data provide convincing evidence against the no hypothesis. So what we want to do here is look at the P value and just determined. Is the P value weird or not? Um, most of the time we looked at the p value and just determine how it compares to a significant level of 1% 5% or 10%. So just looking at the 21% that is not an odd figure that is fairly high for a P value. So I'm going to say since RPI value is fairly large, as compared to a significant level of 10% I'm just putting that and inequality, we cannot reject the null hypothesis. There is not convincing evidence to say that the proportion of lefties at Simon School is any different from the national proportion

What is the formula to find the sample size needed? The formula is given by the formula is given by P cap when pick up is unknown. Okay, When peak cap is unknown, When pickup is unknown, the formula is given by n is equal to Z Alfa by two whole square in 20.25 upon E square. Okay, this should be the farm without when peak app, that is the proportion is unknown. All right, so what is going to be my Alfa by two? I want to find a 99% confidence, right? 99% confidence, Which means my Alfa by two is 0.5 Okay, it is 0.5%. So what is going to be my Z Alfa by two, my Z Alfa by two will become my Z. Everybody will come 2.5758 2.575 in. Well, let's this right. This is 2.575 Okay? And now I want my Toby three. Okay, what does the question say? I want the margin off error off 3% points, so my he should be three. So I'll put my e is equal to three. He is equal to three now, if I put all of these values that I have got in this formula I will get my end, my end as 1844 Right. This will come out to be very close to 1844 This is the sample size now in the second case. Now, in the second case, this is option B or part B. Now I have my P cap as 10% or P cap is equal to P. Cap is equal to 0.1. So automatically, what will be Q cap que capital V 0.9? Because it is one minus 0.1. And what is the formula? The formula is he is equal to are just a moment this is going to be The formula is in is equal to Zen Alfa by two Zad Alfa by two square multiplied by P cap que cap upon e squared upon e square. And I know all of these values My he has to be within 3% points. I will put easy for the three and this time I get my s 6 64. So putting all of these values I get my end is equal to 6 64. Now. The last question says how the results from the two parts will change. If the entire United States is used in sort of California, the numbers will not change. So the results should also not change, so there will be no change and these would be my answers.

So this question start with two groups here, uh, rabbits of 87. And in 92 I'm going to put and the numbers and there are Cougars of very it was gonna be 60. And there was only one Sanders mediation. No. 7.2. Now you're gonna want to So for the standard error of deviation, but which is going to take the square root of the the standard deviation for the first number divided my the first end plus standard deviation of the second number Square Till I did pray. The second hunger plugging these numbers in is gonna be 7.2 squared, divided by 60. Since we have the same numbers, you just gonna do that same thing 7.2 square to buy it. 3 60 She square to that. That's going Teoh Equal Free one. How the Z for 0.1 Just what we're looking for is 2.2. Hey, so too So to solve you, you're gonna subtract 90 to 87. Don't buy in by that number. You just got the plane tree. Why? Just going to get you 3.8162 round 3 22 and 3.82 is greater in 2.8, so therefore, yes, there is significant difference at the 0.1 level.

For this problem were given to random sample sizes. We first tested for athletes and then Brandon members. We were given the mean for both of these mean for athletes. Is 87 in the mean for the band? NUM members is 92. Our sample size, which is n since we had tested two groups of 30 back sample size, is going to be 60 for both. You were also given the standard deviation, which is 7.2 now we're trying to solve for Z at deal that 0.1 to see a syllable significant. The number at on the Z table is 2.58 Now we're gonna want to solve for the standard error of deviation, which that equation equals the square root of the standard deviation for the first number squared, divided by the sample size of the cursed number of the first group. Then you're gonna add the standard deviation of the second group squared, divided by the sample size. For that second group. Plugging in these numbers is going to be the square root of your standard deviation of 7.2 squared, divided by 60 which is our sample size for that first group plus 7.2, which is still our standard deviation for the second group is well square, divided by 60 which is our sample size for the second group. Plugging this into your calculator that will get you 1.31 you're then going to solve for Z by subtracting 92 87 which will get you five. You're going to divide that by 1.31 This is going to get you 3.816 which you can then round 23.82 Now 3.82 is larger than the Z score 2.58 So this means that yes, there is a significant difference at the level 0.1


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