Eye Color Based on a study by Dr. P. Sorita at Indiana Univers...

Question

Eye Color Based on a study by Dr. P. Sorita at Indiana University, assume that 12% of us have green eyes. In a study of 650 people, it is found that 86 of them have green eyes.

b. Is 86 people with green eyes significantly high?

Accepted Answer

Hello, in this video, we are told that during a health survey, it was discovered that 40% of participants are regular yoga practitioners. Out of 500 participants, 230 claimed to practice yoga regularly. We want to determine if this is a significantly high number. So, the first thing we are told that the total amount of participants that practice in the survey is 500. So we are going to label that as N is equal to 500. Furthermore, we are told that 40% of this population are regular yoga practitioners, so we will label that as P, which is equal to 40%, and 40% as a decimal is going to be recalculated as 0.4%. So, in order to approach this problem, the first thing we want to do is you want to find the average amount of people that practice yoga. Now, the average is going to be the mean. Of this population, and that is going to be defined as E equal to the total amount of people multiplied by the probability that they are regular practitioners. Now, in this case here, this is going to be 500 multiplied by 0.4. And this is going to simplify to give us 200. So for the survey, we have a mean of 200. Now what we want to do is we want to get the standard deviation. Of this problem We are going to label the standard deviation. With the variable sigma. Now since we are working with a sample. We want the standard deviation to be defined as sigma is equal to the square root of N times P multiplied by 1 minus P. This is going to give us the square root of the total population, which is 500, multiplied by the probability that they practice yoga regularly, which is 0.4, multiplied by 1 minus the probability, which is 1 minus 0.4. And with the help of a calculator, this is going to approximate to be 10.954. So, now what we want to do is you want to find the Z score for this for this practice or for this survey. Now, in order to determine the Z score, we are going to use the following equation. Z is equal to X minus U divided by sigma. This is saying that if we want to find the Z score, we are going to take the total population, or at least the target population, which is 230, minus the mean and divide this quantity by the standard deviation. That is going to give us 230 minus the mean, which is 200, divided by the standard deviation, which is 10.954, and this is going to simplify to give us a Z score of 2.74. So, this is the Z score of the 230 that regularly practice yoga, or claim to practice yoga on the regular. Now, what we want to determine is if this is a significantly high number. Now, for a normal distribution, the number 2, or anything above 2, so Z greater than 2, is normally considered a significantly high number. And since the Z score that we have is 2.74, and that's greater than 2, then this shows that this is going to be a significantly high number. So, the solution to this problem is going to be A. Yes, This amount of people that claim to practice yoga on the regular is significantly higher than normal. So I hope this video helps you in understanding on how to approach this problem, and I will go ahead and see you all in the next video.

Eye Color Based on a study by Dr. P. Sorita at Indiana University, assume that 12% of us have green eyes. In a study of 650 people, it is found that 86 of them have green eyes.

b. Is 86 people with green eyes significantly high?

Key Concepts

Hypothesis Testing

Significance Level

Proportion and Sample Size

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