EBK UNDERSTANDING BASIC STATISTICS
7th Edition
ISBN: 8220100547560
Author: BRASE
Publisher: CENGAGE L
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Textbook Question
Chapter 3.2, Problem 10P
Critical Thinking: Data Transformation Using Addition In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the data set 5, 9, 10, 11, 15.
(a) Use the defining formula, the computation formula, or a calculator to compute s.
(b) Add 5 to each data value to get the new data set 10, 14, 15, 16, 20. Compute s.
(c) Compare the results of pads (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?
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Students have asked these similar questions
A survey of 581 citizens found that 313 of them favor a new bill introduced by the city.
We want to find a 95% confidence interval for the true proportion of the population who favor the bill.
What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits.
Your Answer:
2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model
below:
1
y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €.
See Question 2, Tutorial 3 for the meaning of the variables in the above model.
The following results are obtained:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.302e+03 4.320e+02 3.015 0.00307
x4
x6
x8
x4:x8
x6:x8
-1.442e+02
2.056e+01 -7.013 1.02e-10
6.340e-01 6.099e+00 0.104 0.91737
-9.455e-02 5.802e-02 -1.630
0.10550
2.882e-02 2.589e-03 11.132
1.673e-03 7.215e-04 2.319
F)
x4
1
3486722
3486722
17.9286 4.214e-05
x6
1
14595537
x8
x4:x8
x6:x8
1
132.4836 < 2.2e-16
1045693
194478
5.3769 0.02191
1 1198603043 1198603043 6163.1900 < 2.2e-16
1 25765100 25765100
1045693
Residuals 135 26254490
Estimated variance matrix
(Intercept)
x4
x6
x8
x4:x8
x6:x8
(Intercept)
x4
x6
x8
x4:x8
x6:x8
0.18875694
1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953
-5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013
-2.322825e+03…
In some applications the distribution of a discrete RV, X resembles the Poisson distribution except that 0 is not a possible value of X. Consider such a RV with PMF
where 1 > 0 is a parameter, and c is a constant.
(a) Find the expression of c in terms of 1.
(b) Find E(X).
(Hint: You can use the fact that, if Y ~ Poisson(1), the E(Y) = 1.)
Chapter 3 Solutions
EBK UNDERSTANDING BASIC STATISTICS
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