4. For a given population of college students, we know that the average monthly
ID: 3309564 • Letter: 4
Question
4. For a given population of college students, we know that the average monthly food expenditure is $136.54 per month, with a standard deviation of $34.50. Suppose we ask 35 college students what their monthly food expenditure is, and calculate the mean. A) What is the probability that the sample mean is greater than $119.652 B) What is the probability that the sample mean is less than $147.32? C) If our sample mean is $127.98, what is the estimation error? D) If our sample mean is $158.46, what is the estimation error? E) What is the probability that the estimation error of our sample mean will be less than $5.84?Explanation / Answer
E(Xbar) = 136.54 , sd(Xbar) = 34.50/sqrt(35) = 5.831564357
Z = (Xbar - 136.54)/5.831564357
a) P(Xbar > 119.65)
= P (Z>2.9)=0.9981
b) P(Xbar < 147.32)
=
P (Z<1.85)=0.9678
c)
Estimation error
The difference between an estimated value and the true value of a parameter or, sometimes, of a value to be predicted.
= 136.54 - 127.98 =8.56
d)
158.56 - 136.54 = 22.02
e) P(|Xbar - 136.54| < 5.84)
= P(|Z| < 5.84/ 5.831564357)
= P(|Z| <1.001446
=
0.6826
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