1) The following graph and regression result gives the (hypothetical) IQ scores for 2 nd graders
and the number of hours they watch TV each week.
Simple linear regression results:
Dependent Variable: IQ
Independent Variable: TV hours/week
IQ = 142.71914 - 3.1612654 TV hours/week
Sample size: ...
MATH 110 FINAL EXAM REVIEW 2023-2024
1) The following graph and regression result gives the (hypothetical)ndIQ
graders
scores for 2
and the number of hours they watch TV each week.
Simple linear regression results:
Dependent Variable: IQ
Independent Variable: TV hours/week
IQ = 142.71914 - 3.1612654 TV hours/week
Sample size: 20
R (correlation coefficient) = -0.86854228
nd
a) Find the predicted IQ for grader
a2 who watches 4 hours of TV per week.
Using the regression equation: IQ = 142.72 – 3.16 (4) = 130.08. The predicted IQ is
nd
approximately 130, for grader
a2 who watches 4 hours of TV per week.
b) Interpret the slope and y-intercept of the regression line in the context of the pro
Slope: The predicted IQ nd
ofgrader
a2 decreases by 3.16 as the number of TV hours per wee
increases by 1.
Y-intercept: The predicted IQndofgrader
a 2 who does not watch TV is approximately 142.7.
c) Interpret the correlation coefficient in the context of the problem.
The correlation coefficient is approximately -0.87. This tells us that is a fairly strong neg
linear association between IQ and TV viewing hours per week.
, 2) According to the Crime in the United States, 1998, 65% of murders are committed w
firearm. Suppose 500 murders are randomly selected.
Note: p=0.65 and n=500
a) What is the mean of the sampling proportion?
The mean of the sampling proportion is 0.65.
b) What is the standard deviation of the sampling proportion?
𝑝(1 − 𝑝)
𝑆𝐷 =
𝑛
0.65 (1 − 0.65)
≈ 0.0213
500
The standard deviation of the sampling proportion is 0.0213.
3) A company produces packets of soap powder labeled “Giant Size 32 Ounces.” The a
weight of soap powder in such a box has a Normal distribution with a mean of 33 oz
standard deviation of 0.7 oz. Suppose that 100 soap boxes are randomly selected.
Note: 𝜇 = 33, 𝜎 = 0.7, 𝑛 = 100
a) What is the mean of the sampling distribution?
The mean of the sampling distribution is 33 oz.
b) What is the standard deviation of the sampling distribution?
𝜎
𝑆𝐷 =
√𝑛
0.7
= 0.07
√100
The standard deviation of the sampling distribution is 0.07.
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