(c) Now suppose that you pick a sample of 25 cars, what is the probability that the sample
mean will exceed 77 mph? Does CLT applies? explain?
5.- In a sample of 200 men, 100 admitted to driving without a seat belt. In a sample of 150
women, 60 admitted to driving without a seat belt. At α = 0.05, is there a difference in the
proportions of men and women driving without a seat belt?(Both Methods)
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M_150_t_2_r_fa_13_h.pdf (3/8)
6.- A Special Forces Military Recruiter claims that the height his recruits have a standard
deviation of 3inches. A sample of 20 of its recruits find that the sample standard deviation is
3.5inches. At α = 0.01, is there enough evidence to support the his claim (Do both methods,
this is a two tailed test)?
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M_150_t_2_r_fa_13_h.pdf (4/8)
7.- Apple claims that the battery life of the iPhone is better than that of the Google phone.
A sample is taken from each company. The Apple sample (n = 26) had a mean of 10hours
and standard deviation of 1hour, while the Google sample (n = 28) had a mean of 9hours
with a standard deviation of 2hours.
(a) Is there a difference in the battery life of the two companies? Use α = 0.01 (Both
Methods)
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M_150_t_2_r_fa_13_h.pdf (5/8)
8.- A new volley-ball shoe manufacturer claims that its shoes increase the vertical jump (in
inches) of any athlete. The following tables shows that result of five athletes with regular
shoes and the new shoes. Is there enough evidence to suggest that there is a difference? Use
α = 0.05.
Table 1: Vertical Jumps in Inches
x1 30 28 27 33
x2 34 29 27 34
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M_150_t_2_r_fa_13_h.pdf (6/8)
9.- Consider the following data.
x
2
3
5
6
9
y
15
15
10
8
3
-x2 -
-y 2 -
-xy-
(a) Find r
(b) Find ŷ
(c) Predict y when x is 4.
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M_150_t_2_r_fa_13_h.pdf (7/8)
Contingency Tables
Step 1 H0 : The row and column variables are Independent
Ha : The row and column variables are Dependent
Step 2
2
χ ∗=
!
(E − O)2
,
E
E=
(row sum) · (column sum)
total sum
Step 3 Find the Rejection Region or P-value
Step 4 Conclusion
Ex: An instructor wishes to see if the way people obtain information
is independent of the educational background. A survey of high school
and college graduates yielded this information. at α = 0.05, test the
claim that the way people obtain information is independent of their
educational background.
- T.V Newspaper Other
High School 150
90
50
College 40
40
30