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3. Answer the following concept questions in 1-3 sentences each. (a) Consider the sampling distribution for X. Suppose X, ~ N(75, 25). Do we need the Central Limit Theorem to find P(X < 72) if our sample size is 9? Why or why not. (b) Consider the sampling distribution for X when we have a "large" sample size (n > 30). When we calculate the z-score, why do we divide by o/n instead of o? (c) Consider the Central Limit Theorem for the difference of means. For our standard deviation, we use SD (X1 - X2) : n2

3. Answer the following concept questions in 1-3 sentences each. (a) Consider the sampling distribution for X. Suppose X, ~ N(75, 25). Do we need the Central Limit Theorem to find P(X < 72) if our sample size is 9? Why or why not. (b) Consider the sampling distribution for X when we have a "large" sample size (n > 30). When we calculate the z-score, why do we divide by o/n instead of o? (c) Consider the Central Limit Theorem for the difference of means. For our standard deviation, we use SD (X1 - X2) : n2

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer part d), e) and f) only.

3. Answer the following concept questions in 1-3 sentences each. (a) Consider the sampling distribution for X. Suppose X; ~ N(75, 25). Do we need the Central Limit Theorem to find P(X < 72) if our sample size is 9? Why or why not. (b) Consider the sampling distribution for X when we have a "large" sample size (n > 30). When we calculate the z-score, why do we divide by a/Vn instead of o? (c) Consider the Central Limit Theorem for the difference of means. For our standard deviation, we use SD (X1 - X2) ni n2 Why don't we want to use 01 02 SD (X1 – X2) %3D (d) Consider the Central Limit Theorem for 1 Proportion. Why do we need to check the success / failure condition? (e) Consider the sampling distribution for S°. What assumption about the population do we need in order to convert S? to a chi-square random variable? (f) Suppose we want to find P(X < 66). For this particular scenario, we have a small sample size (n = 20), and the population standard deviation, o, is unknown. We know the sample standard deviation, s = 9. To perform this calculation, we use the t-distribution. What do we need to assume about the population to make sure we can use the t-distribution? (g) The following question was investigated: If the standard deviation of the mean for the sampling distribution of random samples of size 64 from a large or infinite population is 5, how large must the sample size become if the standard deviation is to be reduced to 0.9. In solving this question, it was determined that n = 1975.308642. Since we cannot talk to a partial person, how many people do we need to sample? (h) Suppose you collect data and want to find P(X < some number) by using the t-distribution. What do we need to assume about the population to make sure we can use the t-distribution? (i) Suppose we want to solve the following:
Transcribed Image Text:3. Answer the following concept questions in 1-3 sentences each. (a) Consider the sampling distribution for X. Suppose X; ~ N(75, 25). Do we need the Central Limit Theorem to find P(X < 72) if our sample size is 9? Why or why not. (b) Consider the sampling distribution for X when we have a "large" sample size (n > 30). When we calculate the z-score, why do we divide by a/Vn instead of o? (c) Consider the Central Limit Theorem for the difference of means. For our standard deviation, we use SD (X1 - X2) ni n2 Why don't we want to use 01 02 SD (X1 – X2) %3D (d) Consider the Central Limit Theorem for 1 Proportion. Why do we need to check the success / failure condition? (e) Consider the sampling distribution for S°. What assumption about the population do we need in order to convert S? to a chi-square random variable? (f) Suppose we want to find P(X < 66). For this particular scenario, we have a small sample size (n = 20), and the population standard deviation, o, is unknown. We know the sample standard deviation, s = 9. To perform this calculation, we use the t-distribution. What do we need to assume about the population to make sure we can use the t-distribution? (g) The following question was investigated: If the standard deviation of the mean for the sampling distribution of random samples of size 64 from a large or infinite population is 5, how large must the sample size become if the standard deviation is to be reduced to 0.9. In solving this question, it was determined that n = 1975.308642. Since we cannot talk to a partial person, how many people do we need to sample? (h) Suppose you collect data and want to find P(X < some number) by using the t-distribution. What do we need to assume about the population to make sure we can use the t-distribution? (i) Suppose we want to solve the following:
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