4.36

a. Two shoes produced by plant A were priced at 55 or higher.

b. histogram
 

20-25	25-30	30-35	35-40	40-45	45-50	50-55	55-60	60-65	35-70

c. The distribution of she prices for plant A is (i) symmetric and (ii) unimodal.

d. The distribution of shoe prices for plant B is (i) symmetric and (iii) bimodal.

e. (i) The direction of extreme is two-sided.

    (ii) The p-value corresponding to the observed price of 55 is (2+2)/20=0.20

    (iii) At the 5% level, the decision is accept Ho.
 
4.72
 

a	(i)	The technique for picking the families at each of the selected centers is convenience sampling.
	(ii)	It is a selection bias.
b	(i)	See histogram below
	(ii)	The distribution is skewed left and unimodal.

40	45	50	55	60	65	70	75	80	85

5.6

a. In a skewed right distribution, which is typical for salary data, the mode or median would generally be less than the mean. The players association would want to focus on showing that most players do not make as much money as thus might prefer reporting the median or mode so they could argue for more money.

b. The owners might prefer reporting the mean, to better reflect the argument for players not needing more money.

5.10

One possible answer is 10, 30 , 40, 60. the smallest and largest observations were made even smaller and larger, respectively, by the same amount , resulting in the same mean but larger variation around the mean.

5.14
 

a	false
b	false
c	true
d	false

5.24
 

a	(iii) 65
b	(iv) remain unchanged

5.26
 

a	Julie had a higher test score
b	(75-70)/5=1. Julie scored 1 standard deviation above the mean of 70
c	(68-62)/4=1.5. Julie scored 1.5 standard deviation above the mean of 62
d	John had a higher test score relative to lecture distribution
e	We can only do that if we knew class size for both lecture 001 and 002

5.34

Yes. For the values 1,3,20, the mean=8 and the s.d.=10.44.

5.36
 

a	True
b	True
c	False, the median is equal to 0
d	False, if all of the values in the data set are the same, removing one of the values will not change the mean.
e	False, if all of the values in the data set are the same, the range and the IQR will both be 0. The range and the IQR for the dataset 2,2,2,2,3,3,4,4,4,4 are also equal.

5.38
 

a	Since fewer means that the difference is negative, from the box plot, we see Q1=0, so 25% are expected to have fewer aircraft.
b	From the box plot, the largest point is about 270 aircraft.
c	From the box plot, Q3 is 100 aircraft.

5.40
 

a	Min=10,Q1=10.5,Median=12,Q3=14,Max=15
b	Launcher C: 20hits.
c	Launcher B: the top 25% was above 16
d	No, we could only give the median since the boxplot displays the five number summary , which includes the median , but not the mean.

5.52
 

a	muscle mass
b	age
c	Stratified random sampling, since within each ago group the responses are somewhat homogeneous (alike) but there are some differences between the age groups (strata).
d	75%
e	100
f	cant tell
g	true
h	false
i	(ii) A women's muscle mass (seems to) decrease with ago.