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Which of the following statements are true?The sampling distribution of p-hat has mean equal to the population proportion p IL. The sampling distribution of p-hat h...

Question

Which of the following statements are true?The sampling distribution of p-hat has mean equal to the population proportion p IL. The sampling distribution of p-hat has standard deviation equal to 'Jnpl-p): The sampling distribution of p-hat is considered close to normal provided that n 2 30.0 |and IIIland IINone of the above gives the complete set of true responses_Il and IlII,Il,and III

Which of the following statements are true? The sampling distribution of p-hat has mean equal to the population proportion p IL. The sampling distribution of p-hat has standard deviation equal to 'Jnpl-p): The sampling distribution of p-hat is considered close to normal provided that n 2 30. 0 |and III land II None of the above gives the complete set of true responses_ Il and IlI I,Il,and III



Answers

Which of the following is a true statement? (A) The sampling distribution of $\hat{p}$ has a mean equal to the population proportion $p$. (B) The sampling distribution of $\hat{p}$ has a standard deviation equal to $\sqrt{n p(1-p)}$ (C) The sampling distribution of $\hat{p}$ has a standard deviation that becomes larger as the sample size becomes larger. (D) The sampling distribution of $\hat{p}$ is considered close toour sample is clearly less than $10 \%$ of all butterfly larvae normal provided that $n \geq 30$. (E) The sampling distribution of $\hat{p}$ is always close to normal.

Okay, uh, for this question, Um, part A and part B there. They all should be correct. Oh, because, um, you know, x bar Ah will convert to them, you know, axe. So that's quite the same to say, Um, the mean off explore is approximately equal to the mean off X, um, part be witches. Basically what, um, central limit their a misstating and heart. See Parsi saying the standard deviation off explore is the same as a senator. Fusion of X, which is stepping though you're wrong by the central. A myth there. Um, we know that the center deviation off X bar should be go to you. The standard deviation off axe over the square. Root off sample size. Um, yeah.

All right, true or false. If each of 25 sample values is equal to 20 minutes, the standard deviation of the sample is zero minutes. This would be true. Since we have all the same values, then there's no variation to be had for any set of sample values. The standard deviation can never be a negative value. That is also true. If the standard deviation of a sample is three, then the variance is nine, and there was one thing that was forgotten here is the units. And when we square stuff, everything is squared inside it. So this should be kilograms squared, not just kilograms, I don't watch those units, so that makes it false at the variance of the sample is 16 seconds squared, then the standard deviation is four seconds, uh correct units are used. So that is true. And if the standard deviation of a sample is 25, then the variance is five cm squared. Uh This is gonna be false. They've got these squares backwards.

All right, so I feature the sample 25 values equal to 20 minutes. The standard deviation of the sample of zero minutes. This is going to be true since there is no different values to be had, therefore no variation. So, for any set of sample values, the standard deviation can never be a negative value. This is true, since standard deviation has to take a square roots, everything inside, and we can't have a negative of a square root, at least on statistics. So that is going to be true. Now, if we have a standard deviation of a sample, that is nine kg, then the variance is nine kg as well. All they did was square the three, but not the kilograms, the variance has to have kilograms squared, so that's going to be false for party. If the variance of a sample is 16 seconds squared, then the standard deviation is four seconds. So what happens if we take the square root of that and square 16 is four seconds squared becomes seconds. So four seconds is the standard deviation, which makes this a true statement. And finally, if the standard deviation of a sample is 25, I believe the centimeters you have centimeters, then the variance is five centimeters squared and that would also be false. Since they mixed up what they square it should be the reverse


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