A.P. Statistics
Review for Semester 2 Exam
Solutions

#1

 ^  p  0.18 p #2
^  p p (1  p)
.18(.82)

 0.0272 n 200

#3
• The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.

#4
• A statistic is unbiased if the expected value of the sample proportion is equal to the true value of the parameter being estimated. The statistic is called an unbiased estimator of the parameter. #5

 _    2.55 x #6


_ 
 0.1626 x n

#7
Approximately normal

#8
Central Limit Theorem
As the size of a SRS increases, the shape of the sampling distribution can be approximated by a normal distribution.
(Typically n  30 )

#9
We are 95% confident that the true mean it takes Malcom to run 2 miles uis between
15.23 and 15.97 minutes.

#10
a) i

b) iii

#11

4.963  0.019

#12
^

m z

*

^

p (1  p ) n (0.5)(0.5)
0.03  1.65 n n  756.25
The sample size must be at least 757

#13
• The t-distribution is bell shaped, but is more spread out and has thicker tails than the zdistribution.
• As the degrees of freedom increases, the t distribution approaches the standard normal distribution. • We use the t distribution when the population standard deviation is unknown.

#14

mz n *

700
100  1.96 n n  188.24
The sample size must be at least 189

#15
• Simple Random Sample

#16

H 0 : p  0.35
H a : p  0.35

#17
a) Reject the hypothesis that the mean change of sugar levels is 15 mg/dl when it is really 15 mg/dl. b) Reject the hypothesis that the mean change of sugar levels is more than 15 mg/dl when it really is more than 15 mg/dl.

#18
(i) Increase 
(ii) Increase n
(iii) Decrease 
(iv) Consider a particular H a further away from
H 0 (in the direction of H ). a #19
.05

#20
.22

#21
The probability, assuming H 0 is true, that the observed outcome would take a value as extreme or more extreme than that actually observed. #22
• To find out if there is a meaningful linear relationship between two variables.
• Usually (but not always), the null hypothesis is
H o :   0 (There is no relationship between the two variables)

#23
H 0 : p  0.6
H a : p  0.6 p = The true proportion of shots Pablo makes when playing basketball.

#24 z = -2.041

#25 p-value: 0.0206

#26
• Since our p-value of 0.0206 is greater than
  0.01 , we fail to reject H o and thus disagree with John’s claim.

#27
• Since our p-value of 0.0206 is less than
  0.05 , we reject H o and thus disagree with