ECON 221 Harvard Confidence Interval Estimate for The Proportion Economics Questions

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ECON 221–Statistics for Economics and Business I
Third Excel Assignment
Due on Moodle on Tuesday, April 13, 2021 at 2:00 PM.
Each of the following problems uses a procedure that can be found in the PHStat menu, two of
them are under Confidence Intervals and one is under Sample Size. The main differences among
them are:
? one is an estimate of the population mean and sigma is unknown.
? one is an estimate of the population proportion.
? in one you are determining the sample size for estimating the population mean.
Each part relies on the data in your Housing and Donations datafile.
A. Using PHStat/Excel, estimate the population mean level of annual charitable donations at
the 99% confidence level. Remember: you do NOT know what the standard deviation of
the population of donations is. (5 points)
B. Using PHStat/Excel, estimate the population proportion of all respondents who think
their housing situation is “Comfortable and Safe” at the 95% confidence level. (5 points)
C. If we were to conduct a survey to determine the mean annual housing expenses for ALL
households in the US, how large a sample should we take if we want the point estimate
(sample mean) to be within $500 of the true population mean, at the 95% confidence
level? Use PHStat/Excel to determine this sample size. (5 points)
What is
your
gender?
Male
Male
Male
Male
Female
Male
Female
Female
Male
Male
Male
Male
Male
Male
Female
Male
Male
Female
Female
Female
Male
Female
Male
Female
Male
Male
Female
Male
Female
Female
Female
Male
Female
Female
Female
Female
Male
Male
Male
Female
Female
Female
How would you describe
your current housing
situation?
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
How would you classify your
annual household income?
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
above $150,000
above $50,000 to $100,000
above $100,000 to $150,000
$0 to $50,000
above $150,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
above $50,000 to $100,000
above $100,000 to $150,000
above $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
above $100,000 to $150,000
above $150,000
above $100,000 to $150,000
above $150,000
above $150,000
Give an estimate of your annual
household housing expenses
(rent or mortgage payment.
0
0
0
400
10,000
1,000
25,000
10,000
80,000
9,000
10,000
3,000
0
5,000
700
400
100,000
70,000
1,000
6,000
0
1,000
100,000
4,800
5,000
680
14,400
7,000
1,000
968
800
20,000
25,000
9,000
800
9,000
14,000
30,000
60,000
40,000
4,800
24,000
Female
Female
Male
Female
Female
Female
Female
Female
Male
Male
Male
Female
Male
Male
Female
Male
Male
Female
Female
Female
Male
Female
Female
Female
Female
Male
Female
Female
Male
Female
Male
Female
Male
Female
Female
Female
Male
Female
Female
Female
Male
Male
Male
Female
Female
Female
Male
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
above $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $150,000
above $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $150,000
above $150,000
above $50,000 to $100,000
above $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
above $150,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
10,000
10,000
0
35,000
1,200
900
0
6,000
1,500
20,000
10,800
15,600
13,000
1,100
20,000
30,000
16,000
20,000
0
0
1,900
500
30,000
8,000
10,000
10,000
18,000
35,000
100,000
1,600
40,000
30,000
30,000
10,000
10,000
10,000
130,000
1,000
14,000
12,000
10,000
12,000
20,000
18,000
7,500
500
24,000
Female
Male
Male
Male
Male
Male
Male
Female
Male
Female
Female
Female
Female
Female
Female
Male
Female
Female
Male
Female
Female
Female
Female
Male
Male
Female
Female
Male
Female
Female
Female
Female
Female
Female
Male
Male
Male
Male
Male
Female
Male
Male
Female
Female
Male
Male
Male
Comfortable and safe
Cramped and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Cramped and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Cramped and unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
above $150,000
$0 to $50,000
above $100,000 to $150,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
above $150,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $50,000 to $100,000
above $50,000 to $100,000
above $100,000 to $150,000
$0 to $50,000
above $100,000 to $150,000
above $150,000
$0 to $50,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $100,000 to $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $50,000 to $100,000
above $150,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
above $150,000
above $100,000 to $150,000
$0 to $50,000
above $50,000 to $100,000
above $150,000
$0 to $50,000
18,000
25,000
7,000
2,500
0
1,000
1,000
2,500
500
0
850
4,500
12,000
500
6,000
6,350
3,200
30,000
12,000
30,000
27,600
1,500
21,600
10,000
18,000
7,000
11,000
22,000
7,200
21,600
6,000
20,000
0
16,800
550
40,000
40,000
0
5,000
450
1,500
2,310
3,900
13,200
2,000
50,000
4,000
Male
Male
Female
Female
Female
Female
Female
Female
Male
Male
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Male
Female
Female
Female
Male
Female
Female
Female
Male
Female
Male
Female
Male
Female
Male
Male
Female
Male
Female
Female
Female
Female
Female
Female
None of the above
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Cramped and unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Cramped and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and unsafe
Comfortable and safe
Cramped and unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
above $50,000 to $100,000
$0 to $50,000
above $100,000 to $150,000
$0 to $50,000
above $100,000 to $150,000
above $100,000 to $150,000
$0 to $50,000
above $50,000 to $100,000
above $100,000 to $150,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $50,000 to $100,000
$0 to $50,000
above $100,000 to $150,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
above $150,000
above $50,000 to $100,000
above $50,000 to $100,000
above $100,000 to $150,000
above $150,000
$0 to $50,000
above $100,000 to $150,000
$0 to $50,000
above $100,000 to $150,000
above $150,000
above $100,000 to $150,000
$0 to $50,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
above $50,000 to $100,000
15,000
8,000
6,000
20,000
15,000
12,000
10,000
20,000
25,000
1,500
15,600
5,500
11,400
13,200
1,300
3,600
800
2,300
10,000
6,300
20,124
1,300
1,800
14,000
6,000
12,000
15,000
850
600
20,400
6,500
1,100
2,200
3,000
450
50,000
3,500
200,000
30,000
24,000
8,000
5,268
10,000
6,000
4,500
9,300
860
Female
Female
Female
Male
Female
Male
Male
Female
Female
Female
Male
Male
Male
Female
Female
Female
Female
Female
Female
Male
Male
Female
Male
Female
Male
Male
Male
Male
Male
Male
Female
Female
Female
Male
Male
Female
Female
Female
Female
Female
Female
Male
Female
Male
Female
Male
Female
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Cramped and unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Cramped and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
above $100,000 to $150,000
$0 to $50,000
above $50,000 to $100,000
above $100,000 to $150,000
$0 to $50,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
above $150,000
above $150,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
above $100,000 to $150,000
above $50,000 to $100,000
1,000
6,000
12,000
15,600
4,200
10,000
7,200
9,000
5,400
19,200
5,400
700
7,000
7,800
750
1,135
12,000
7,600
4,200
6,000
0
0
1,000
6,000
0
500
0
10,000
17,500
5,060
12,000
40,000
1,200
6,500
0
10,000
3,500
11,000
900
250
500
8,000
8,200
19,440
500
1,500
400
Female
Male
Male
Male
Male
Female
Male
Female
Female
Male
Male
Male
Male
Male
Female
Female
Female
Female
Male
Female
Male
Male
Female
Female
Male
Female
Female
Male
Female
Male
Female
Female
Male
Female
Comfortable but unsafe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
$0 to $50,000
$0 to $50,000
above $150,000
above $150,000
above $150,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
above $100,000 to $150,000
$0 to $50,000
above $100,000 to $150,000
above $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
above $100,000 to $150,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $50,000 to $100,000
$0 to $50,000
6,000
8,000
20,000
66,000
160,000
2,000
1,500
20,448
20,000
1,000
100,000
12,000
1,200
15,000
2,500
1,000
21,600
44,000
10,000
28,000
8,000
6,000
625
7,200
6,000
7,200
7,500
1,200
2,500
5,000
3,500
7,200
5,000
8,000
Give an estimate of
your annual
household
charitable
donations.
500
0
0
50
2,000
1,000
10,000
3,000
500
200
900
1,000
0
1,000
100
0
2,000
1,000
0
0
5,000
1,000
200
0
500
0
500
0
500
0
1,000
7,500
2,000
30,000
100
2,000
1,200
500
5,000
10,000
5,000
6,000
2,000
2,000
100
20,000
500
500
800
1,000
200
1,200
1,500
500
4,000
1,000
0
5,000
1,500
1,000
100
0
7,000
100
5,000
4,000
1,000
50
2,000
5,000
10,000
200
0
0
10,000
0
100
100
145,000
50
600
200
300
100
450
200
50
0
1,200
800
1,500
100
0
0
100
100
1,000
50
0
500
50
3,000
200
20
300
2,000
8,000
0
8,000
1,500
3,000
1,200
1,000
4,000
1,500
2,000
4,500
2,000
1,200
80
5,000
1,500
3,000
100
5,000
5,000
0
1,000
100
1,000
50
28
0
0
5,000
0
3,000
250
200
2,000
500
250
500
1,000
2,500
100
200
150
400
500
1,500
400
300
500
500
1,200
1,000
0
500
200
50
2,000
500
500
300
200
500
1,000
1,000
1,500
200
0
10
100,000
10,000
3,000
25,000
0
1,000
200
450
600
0
500
750
250
1,000
600
700
200
100
200
250
300
3,000
100
500
15
0
0
300
0
1,000
0
500
100
2,000
50
0
0
0
500
200
300
5,000
25
0
0
100
1,000
150
0
50
0
300
50
0
1,000
1,000
100
0
0
5,000
7,500
3,500
500
2,000
1,000
1,500
0
500
2,500
0
3,000
3,000
1,000
200
750
2,000
1,000
25
50
520
75
100
100
0
100
500
1,000
100
100
0
1,000
Last Name Begin on This Row in the Table fo Random Digits
Ahmed, Nusrat
1
Aldhomeiry, Nader F.
2
Alhashemi, Laythai
3
Augusto, Tiffany A.
4
Connors, John T.
5
Edwards, Zachary J.
6
Fulton, Charles W.
7
Galey, Nickolas J.
8
Grullon, Katherine
9
Herrera de Jesus, Mariely
10
Knapp, Elijah T.
11
Knoll, Emma G.
12
Kochanski, Kara
13
Maciejaszek, Lynsey E.
14
Mcguire, Deaglan
15
Mihalko, Samantha A.
16
Moore, Tyler
17
Orlando, Casey R.
18
Poulson, Enzo
19
Quaglia, Connor
20
Walker, Rachel J.
21
Weidow, Isabella H.
22
Yelland, Tyler M.
23
Zazzera, Michael D.
24
What is your gender?
Male
Male
Male
Male
Male
Male
Male
Male
Male
Male
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
Female
How would you describe
your current housing
situation?
Comfortable but unsafe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Cramped and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Cramped and unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable but unsafe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Comfortable and safe
Number with housing that is
comfortable and safe (from
the sample)
n (number of trials)
p (probability of success)
How would you classify your
annual household income?
$0 to $50,000
above $100,000 to $150,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $150,000
above $50,000 to $100,000
above $50,000 to $100,000
above $50,000 to $100,000
$0 to $50,000
$0 to $50,000
$0 to $50,000
above $100,000 to $150,000
$0 to $50,000
above $50,000 to $100,000
above $100,000 to $150,000
above $100,000 to $150,000
above $50,000 to $100,000
above $100,000 to $150,000
above $50,000 to $100,000
above $150,000
above $50,000 to $100,000
above $100,000 to $150,000
19
25
0.76
BINOMIAL DISTRIBUTION TABLE
X (number with housing that
is comfortable and safe)
Probability of X
Cumulative Probability of X
0
1
2
3
4
3.20097E-16
2.5341E-14
9.62957E-13
2.33785E-11
4.07175E-10
3.20097E-16
2.56611E-14
9.88618E-13
2.43671E-11
4.31542E-10
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
5.41543E-09
5.71628E-08
4.91328E-07
3.50071E-06
2.09394E-05
0.000106093
0.00045813
0.001692535
0.005359694
0.014547741
0.033783087
0.06686236
0.112092781
0.15776021
0.184053578
0.174850899
0.131832027
0.075903288
0.031351358
0.008273275
0.001047948
5.84697E-09
6.30098E-08
5.54338E-07
4.05505E-06
2.49945E-05
0.000131088
0.000589217
0.002281752
0.007641446
0.022189187
0.055972275
0.122834635
0.234927416
0.392687626
0.576741204
0.751592103
0.88342413
0.959327418
0.990678777
0.998952052
1
Give an estimate of your
annual household housing
expenses (rent or mortgage
payment.
0
400
10,000
10,000
80,000
1,100
15,600
3,000
25,000
30,000
30,000
6,000
450
6,000
15,600
18,000
600
15,600
0
6,000
20,124
6,000
4,800
30,000
9,000
Give an estimate of your
annual household
charitable donations.
0
0
50
300
500
1,000
1,000
1,500
1,500
10,000
0
20
100
200
200
200
300
500
800
1,000
1,000
2,000
5,000
5,000
30,000
In the sample there are 19 people that reported being comfortable and safe. The probability of having
a housing situation “comfortable and safe” is calculated by dividing the number of people that
reported being in that situatiion (19) by the total number of people in the sample (25). The probability
is .76 or 76%.
X represent the number of people in the housing situation “comfortable and safe” of which we want to
know the probability.
Binomial Distribution
Housing Situation – Comfortable and Safe
Probability of X
0.2
0.15
Probability of X
0.1
0.05
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
X
bility of having
The probability
hich we want to
‘How would you describe your current housing situation?
Row tags
Column tags
Comfortable and safe
Female
52.00%
Male
Total
24.00%
76.00%
‘How would you classify your annual household income?
Row tags
Comfortable and safe
Comfortable but unsafe
Cramped and safe
Cramped and unsafe
Total
Column tags
$0 to $50,000
16.00%
4.00%
4.00%
4.00%
28.00%
Comfortable but unsafe
Cramped and safe
Cramped and unsafe
Total
4.00%
0.00%
4.00%
60.00%
4.00%
8.00%
12.00%
12.00%
0.00%
4.00%
40.00%
100.00%
above $100,000 to $150,000
32.00%
0.00%
0.00%
0.00%
32.00%
above $150,000 above $50,000 to $100,000
8.00%
20.00%
0.00%
4.00%
0.00%
8.00%
0.00%
0.00%
8.00%
32.00%
Total
76.00%
8.00%
12.00%
4.00%
100.00%
Joint Probabilities
Marginal Probabilities
NormalDistribution
5.97322E-05
5.97322E-05
5.97322E-05
5.98104E-05
5.99266E-05
6.01176E-05
6.04895E-05
6.04895E-05
6.04895E-05
6.08477E-05
6.08477E-05
6.15216E-05
6.15216E-05
6.24229E-05
6.29479E-05
6.29479E-05
6.29479E-05
6.29479E-05
6.39838E-05
6.39838E-05
6.46089E-05
5.96283E-05
5.96283E-05
3.07711E-05
2.97422E-09
Average
2486.8
St. Deviation
6155.446585
Distribution of “Donations”
0.00007
0.00006
0.00005
Probability
Donations
0.00
0.00
0.00
20.00
50.00
100.00
200.00
200.00
200.00
300.00
300.00
500.00
500.00
800.00
1000.00
1000.00
1000.00
1000.00
1500.00
1500.00
2000.00
5000.00
5000.00
10000.00
30000.00
0.00004
0.00003
0.00002
0.00001
0
0.00
5000.00
10000.00
15000.00
Donations ($)
The data does not show characteristics of a normal distributio
distribution should be bell shaped. That is with the center in th
left and right tails and symetric.
tion of “Donations”
15000.00
20000.00
25000.00
Donations ($)
cs of a normal distribution. A normal
at is with the center in the middle,
30000.00

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Sample mean

Annual Housing Expenses

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