Question

31. Cholesterol The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean 188 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl. For 14-year-old boys, blood cholesterol levels follow a Normal distribution with mean 170 mg/dl and standard deviation 30 mg/dl. Suppose we select independent SRSs of 25 men aged 20 to 34 and 36 boys aged 14 and calculate the sample mean cholesterol levels x?? and x??. (a) What is the shape of the sampling distribution of x?? - x??? Why? (b) Find the mean of the sampling distribution. Show your work. (c) Find the standard deviation of the sampling distribution. Show your work.

          31. Cholesterol The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean 188 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl. For 14-year-old boys, blood cholesterol levels follow a Normal distribution with mean 170 mg/dl and standard deviation 30 mg/dl. Suppose we select independent SRSs of 25 men aged 20 to 34 and 36 boys aged 14 and calculate the sample mean cholesterol levels x?? and x??.
(a) What is the shape of the sampling distribution of x?? - x??? Why?
(b) Find the mean of the sampling distribution. Show your work.
(c) Find the standard deviation of the sampling distribution. Show your work.

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31. Cholesterol The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean 188 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl. For 14-year-old boys, blood cholesterol levels follow a Normal distribution with mean 170 mg/dl and standard deviation 30 mg/dl. Suppose we select independent SRSs of 25 men aged 20 to 34 and 36 boys aged 14 and calculate the sample mean cholesterol levels x?? and x??.
(a) What is the shape of the sampling distribution of x?? - x??? Why?
(b) Find the mean of the sampling distribution. Show your work.
(c) Find the standard deviation of the sampling distribution. Show your work.

Added by Jeffery D.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Prabhakar Kumar

01/31/2023

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- The cholesterol levels for men aged 20 to 34 follow a normal distribution with mean \( \mu_M = 188 \) mg/dl and standard deviation \( \sigma_M = 41 \) mg/dl. - The cholesterol levels for 14-year-old boys follow a normal distribution with mean \( \mu_B = 170 \) Show more…

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Cholesterol: The level of cholesterol in the blood for all men aged 20 to 34 follows a normal distribution with a mean of 188 milligrams per deciliter (mg/dl) and a standard deviation of 41 mg/dl. For 14-year-old boys, blood cholesterol levels also follow a normal distribution with a mean of 170 mg/dl and a standard deviation of 30 mg/dl. Suppose we select independent simple random samples (SRSs) of 25 men aged 20 to 34 and 36 boys aged 14, and calculate the sample mean cholesterol levels, x̄ᴹ and x̄ᵇ. (a) What is the shape of the sampling distribution of x̄ᴹ - x̄ᵇ? Why? (b) Find the mean of the sampling distribution. Show your work. (c) Find the standard deviation of the sampling distribution. Show your work.

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00:01 In this video we are going to focus on finding the shape of the sampling distribution based on the given information about the cholesterol level in blood for all men aged between 20 to 34.

00:12 So here we can write that sample size for the first sample is equal to 25 and then we can say that sample size for the second sample is equal to 36 and then here the mean value for first sample will be equals to 188 then we have the value of mean for second sample to be equal to 170 and then the value of standard deviation for the first sample is 4 -1 and standard deviation for the second sample is equal to 30.

00:41 Now here we have to understand that we are taking the xm value to be here equals to x1 and it will be here we can write that the value of x bar b so b refers to boys and m refers to men.

00:58 So it will be here equals to x2.

01:01 So here whatever we have written that is for second sample, it is for group of sample of boys and whatever we have written for one, it is for men.

01:10 Now here we can say that we have been given that population distribution of the first population is a normal and it is also given that the population distribution of second population is also normal.

01:23 Now since both, let's write over here that since both and then it will be population.

01:31 Here it will be p -o -p -u -l -a -t -i -o -n.

01:34 Have a normal distribution and it can be written over here.

01:39 Normal distribution.

01:41 That is, they have a normal d -i -s -t -r -i -b -u -t -i -o -n...

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