Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Given a population mean of 53.7 with a standard deviation of 1.3 and a sample size

of 6, answer these questions:

Part A: What is the standard deviation of the sampling distribution of X? Show your

work. (5 points)

Part B: What does the sample size need to be if you want the standard deviation of

the sampling distribution of x to be 0.325? Show your work. (5 points) (10 points)

Sagot :

JeanaShupp

Answer: A. 0.4899 B. 14

Step-by-step explanation:

If X = random variable

then, the standard deviation of the sampling distribution of X = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

A.

GIven: [tex]\sigma= 1.2, \n= 6[/tex]

The standard deviation of the sampling distribution of X = [tex]\dfrac{1.2}{\sqrt{6}}=0.4899[/tex]

B. Let n be the sample size,

[tex]0.325=\dfrac{1.2}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=\dfrac{1.2}{0.325}\\\\\Rightarrow\ \sqrt{n}=3.69230769231\\\\\Rightarrow\ n= (3.69230769231)^2=13.6331360947\approx 14[/tex]

Hence, the required sample size = 14

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.