Question

5 part a) The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 85 have PC's at home. Find the rejection region for this test using α = 0.10.

A) Reject H0 if z > 1.645 or z < -1.645.

B) Reject H0 if z = 1.28.

C) Reject H0 if z < -1.28.

D) Reject H0 if z > 1.28.

part b) A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normally distributed. Find the 95% confidence interval for the true mean. $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00

A) ($1.35, $2.85)

B) ($3.39, $6.01) C)

($2.11, $5.34) D)

($4.81, $6.31)

part c) Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of senior citizens whose net worth is too high to qualify for government health care but who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:

71 76 69 79 89 77 64 92 68 93 72 95 79 65 84 66 71 84 73 76 63 90 78 67 85 Find Q1 of the data.

A) 68

B) 76.5

C) 69

D) 68.5

part d) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a ten, a king or a diamond. Round to the nearest hundredth.

A) 0.37

B) 0.31

C) 0.29

D) 0.40

Answer 1

(a)

Here, Ho: Proportion =35% and Ha: Prop > 35%

Right tailed test.

Hence; Critical Value of Z (Right Tailed): 1.28

ANS: D) Reject H0 if z > 1.28.

(b) sample mean = sum of terms / no of terms = 47/10 = 4.7

sample sd = s

data	data-mean	(data - mean)2
3.60	-1.1	1.21
4.50	-0.2	0.04
2.80	-1.9	3.61
6.30	1.6	2.56
2.60	-2.1	4.41
5.20	0.5	0.25
6.75	2.05	4.2025
4.25	-0.45	0.2025
8.00	3.3	10.89
3.00	-1.7	2.89

CI = mean +/- E

CI = 4.7 + /- 1.312 = (3.39 ,  6.01)

ANS: B) ($3.39, $6.01)

(c)

The first quartile is the median of the bottom half of the numbers.

Nos in ascending order:

63   64   65   66   67   68   69   71   71   72   73   76   76   77   78   79   79   84   84   85   89   90   92   93   95   

Bottom half is

63   64   65   66   67   68   69   71   71   72   73   76   

The median of these numbers is 68.5.

ANS: D) 68.5

(d) P( 10 or king or diamond)

no of 10s = 4

no of kings = 4

no of diamonds = 13

Also ther is one 10 and one king in diamond

P( 10 or king or diamond) = (4 + 4 + 13 - 2) / 52 = 0.37

ANS: A) 0.37