Unformatted text preview: found a job within one year of graduating from college.
(f) If we increased the conﬁdence level what would happen to the width of the interval, i.e. how
would the precision of the interval change. (Hint: You do not need to calculate the interval to
answer this question.)
Increasing the conﬁdence level would increase the margin of error hence widen the interval, i.e.
the interval would loose precision.
(g) If we increased the sample size what would happen to the width of the interval, i.e. how would
the precision of the interval change. (Hint: You do not need to calculate the interval to answer
this question.)
Increasing the sample size would decrease the margin of error hence make the interval narrower,
i.e. the interval would gain precision.
10. In a poll conducted by Survey USA on July 12, 2010 70% of the 119 respondents between the ages of
18 and 34 said they will vote in the November 2010 midterm election for Prop 19 which would change
California law to legalize marijuana and allow it to be regulated and taxed. At a 95% conﬁdence level
this sample has an 8% margin of error. Based on this information which of the following statements
is (are) true?
(a) We are 95% conﬁdent that between 62% and 78% of the California voters in this sample support
support Prop 19.
(b) We are 95% conﬁdent that between 62% and 78% of all California voters between
the ages of 18 and 34 support Prop 19.
(c) In 95% of the random samples of size 119 of California voters between the ages of 18 and 34 the
proportion who plan to vote for Prop 19 will be between 62% and 78%.
(d) Based on this conﬁdence interval there is suﬃcient evidence to suggest that majority
of California voters between the ages of 18 and 34 support Prop 19.
11. Scientists studied the relationship between the length of the body of a bullfrog and how far it can
jump. Mean body length is 149.64 mm and the standard deviation is 14.47 mm. The mean maximum
7 jump is 103.99 cm and the standard deviation is 17.94 cm. The correlation between body length and
maximum jump is 0.28.
(a) What is the equation of the regression line to predict maximum jump based on body length?
slope = 0.28 ∗ 17.94 = 0.35
14.47
intercept = 103.99 − 0.35 ∗ 149.64 = 51.62
y = 51.62 + 0.35x
ˆ
(b) Interpret the slope in context.
For a millimeter increase in the body length of a bull frog, maximum jump is expected on average
to increase by 0.35 cm.
(c) Interpret the intercept in context.
A bullfrog that is 0 mm in length is expected to have a maximum jump of 51.62 cm. This obviously
does not make sense.
(d) What is r2 ? Interpret in context.
r2 = 0.282 = 0.0784. 7.84% of the variation in maximum jump is explained by body length.
(e) If a frog who is 155 mm jumps 110 cm, will it have a positive or negative residual?
y = 51.62 + 0.35 ∗ 155 = 105.87cm
ˆ
Residual = Observed  Predicted = y − y = 110 − 105.87 = 4.13 → Positive
ˆ
(f) Does this study show that longer body length causes greater maximum jump? Why, why not?
No, there may be other conf...
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