Fund raising DatabaseQuestion: Mr. Smith has asked you to answer the below questions using the Fundraising Database posted below. The database is a sample of the history of donors that have contributed to your company. It includes many variables about the demographics of the donors and the amount they have donated.What is an interval estimate of the average donation for the population based off this sample?What is an interval estimate of the proportion of donors that are home owners for the population based off this sample?Is there a significant difference between the mean maximum donation between donors that own a home and those that do not own a home? Assume unequal variances.We want to make a claim that the average donation is $13 for the population. Does this sample provide evidence against that claim?Conduct appropriate confidence intervals and hypothesis tests at 95% confidence (5% significance) to answer these questions and summarize the results for Mr. Smith. Within each question, add some explanations about how did you come up with the response? What analysis did you use and what was the output? If you conducted a hypothesis test, what were your hypotheses? What would be your conclusion to the question? What is your recommendation to your manager Mr. Smith? Row IdHomeowner (1=Yes)Gender (1=Female)Home Value ($1000s)Income ($100s)Number PromotionsLargest Gift ($)Latest Gift ($)Average Time Between Gifts (Month)Average Gift1111399703746534.85714285721069846346121269.43018283763210574.28571428641014715469410837.0851054743220111167.66666666761148227538101037.3711857498472020310.6923076981013554977715739.57692307791050538851151089101114385332116166131111131657566127161211428271736373.65909090913116294725953123.652173913140013184582510102815001052402272020716.666666671611779500987714.3448275861710807393601010109.09090909118102246640763432314.555555561910789398486042631.752001995407832510613.62110936590696523.6296296322118603923820508.83333333323113510633221515312.52401735455589966.076923077251018884359823133517.526113958862532020311.927114112731515155152810610328502510510.06252911826514371515683011780354482015913.46153846310041834892151458.45454545532013321536662020109.4444444443310186838028101035.1666666673401457329851010123.5909090913510160443126101068.75361184255650101045.94444444437112085797505564.722222222381055051142241613613391181942826101045.64010002710106104111296315645272.2608695654210299315222013411.7543006754022416169134411998354721051264510568216211212310.66666667460062040552151169.727272727471031420776252541248004347454331010564900470324292020514.8

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.2: Representing Data

Problem 22PFA

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Fund raising Database

Question: Mr. Smith has asked you to answer the below questions using the Fundraising Database posted below. The database is a sample of the history of donors that have contributed to your company. It includes many variables about the demographics of the donors and the amount they have donated.

What is an interval estimate of the average donation for the population based off this sample?
What is an interval estimate of the proportion of donors that are home owners for the population based off this sample?
Is there a significant difference between the mean maximum donation between donors that own a home and those that do not own a home? Assume unequal variances.
We want to make a claim that the average donation is $13 for the population. Does this sample provide evidence against that claim?

Conduct appropriate confidence intervals and hypothesis tests at 95% confidence (5% significance) to answer these questions and summarize the results for Mr. Smith.

Within each question, add some explanations about how did you come up with the response? What analysis did you use and what was the output? If you conducted a hypothesis test, what were your hypotheses? What would be your conclusion to the question? What is your recommendation to your manager Mr. Smith?

Row Id	Homeowner (1=Yes)	Gender (1=Female)	Home Value ($1000s)	Income ($100s)	Number Promotions	Largest Gift ($)	Latest Gift ($)	Average Time Between Gifts (Month)	Average Gift
1	1	1	1399	703	74	6	5	3	4.857142857
2	1	0	698	463	46	12	12	6	9.4
3	0	1	828	376	32	10	5	7	4.285714286
4	1	0	1471	546	94	10	8	3	7.08
5	1	0	547	432	20	11	11	6	7.666666667
6	1	1	482	275	38	10	10	3	7.3
7	1	1	857	498	47	20	20	3	10.69230769
8	1	0	1355	497	77	15	7	3	9.576923077
9	1	0	505	388	51	15	10	8	9
10	1	1	1438	533	21	16	16	6	13
11	1	1	1316	575	66	12	7	1	6
12	1	1	428	271	73	6	3	7	3.659090909
13	1	1	629	472	59	5	3	12	3.652173913
14	0	0	1318	458	25	10	10	2	8
15	0	0	1052	402	27	20	20	7	16.66666667
16	1	1	779	500	98	7	7	1	4.344827586
17	1	0	807	393	60	10	10	10	9.090909091
18	1	0	2246	640	76	34	32	3	14.55555556
19	1	0	789	398	48	60	42	6	31.75
20	0	1	995	407	83	25	10	6	13.6
21	1	0	936	590	69	6	5	2	3.62962963
22	1	1	860	392	38	20	5	0	8.833333333
23	1	1	3510	633	22	15	15	3	12.5
24	0	1	735	455	58	9	9	6	6.076923077
25	1	0	1888	435	98	23	13	35	17.5
26	1	1	3958	862	53	20	20	3	11.9
27	1	1	411	273	15	15	15	5	15
28	1	0	610	328	50	25	10	5	10.0625
29	1	1	826	514	37	15	15	6	8
30	1	1	780	354	48	20	15	9	13.46153846
31	0	0	418	348	92	15	14	5	8.454545455
32	0	1	3321	536	66	20	20	10	9.444444444
33	1	0	1868	380	28	10	10	3	5.166666667
34	0	1	457	329	85	10	10	12	3.590909091
35	1	0	1604	431	26	10	10	6	8.75
36	1	1	842	556	50	10	10	4	5.944444444
37	1	1	2085	797	50	5	5	6	4.722222222
38	1	0	5505	1142	24	16	13	6	13
39	1	1	819	428	26	10	10	4	5.6
40	1	0	0	0	27	10	10	6	10
41	1	1	296	315	64	5	2	7	2.260869565
42	1	0	299	315	22	20	13	4	11.75
43	0	0	675	402	24	16	16	9	13
44	1	1	998	354	72	10	5	12	6
45	1	0	568	216	21	12	12	3	10.66666667
46	0	0	620	405	52	15	11	6	9.727272727
47	1	0	314	207	76	25	25	4	12
48	0	0	4347	454	33	10	10	5	6
49	0	0	470	324	29	20	20	5	14.8

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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