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Refer to Exercise 37.

a. Find the probability of getting a difference in sample means xM-xBthat鈥檚 less than 0mg/dl.

b. Should we be surprised if the sample mean cholesterol level for the 14-year-old boys exceeds the sample mean cholesterol level for the men? Explain your answer.

Short Answer

Expert verified

Part a. The probability is 0.0307

Part b. Yes

Step by step solution

01

Part a. Step 1. Given information

From the previous exercise, we have:

=18=9.6042x=0

02

Part a. Step 2. Explanation

The z score is the value decreased by the mean and divided by the standard deviation. Then we have,

z=x-=0-189.6042=-1.87

Now we will determine the value of the probability, that is:

P(xM-xB<0)=P(Z<-1.87)=0.0307=3.07%

03

Part b. Step 1. Explanation

It is given that:

z=x-=0-189.6042=-1.87

And the probability is 0.3070

Thus, a probability is considered to be small when the probability is less than 0.05.

We then note that the probability of the mean differencexM-xB being less than zero is small which means that it is unlikely that the mean difference is negative and thus we would be surprised if the sample mean cholesterol level for the fourteen year old boys exceeds the sample exceeds the sample mean cholesterol level for the mean. Thus, yes we should be surprised.

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