Question: Using your CardioGoodFitness sample dataset, is there a significant difference in average age between single and partnered customers?Use alpha = 0.05 to answer this question. State your hypotheses, results, and interpretation. Extra Background info :  

CardioGood Fitness is a developer of high-quality cardiovascular exercise equipment.Its products include treadmills, fitness bikes, elliptical machines, and e-glides. CardioGood Fitness looks to increase the sales of its treadmill products and has hired the AdRight Agency, a small advertising firm, to found and implement an advertising program. The AdRight Agency plans to identify particular market segments that are most likely to buy their client's goods and services and then locate advertising outlets that will reach that market group. This activity includes collecting data on clients' actual sales and on the customers who make the purchases, with the goal of determining whether there is a distinct profile of the typical customer for a particular product or service.If a distinct profile emerges, efforts are made to match that profile to advertising outlets known to reflect the particular profile, thus targeting advertising directly to high-potential customers.

CardioGood Fitness sells three different lines of treadmills. The TM195 is an entry-level treadmill. It is as dependable as other models offered by CardioGood Fitness, but with fewer programs and features. It is suitable for individuals who thrive on minimal programming and the desire for simplicity to initiate their walk or hike. The TM195 sells for $1,500.

The middle-line TM498 adds to the features of the entry-level model two user programs and up to 15% elevation upgrade. The TM498 is suitable for individuals who are walkers at the transitional stage from walking to running or midlevel runners. The RM498 sells for $1,750.

The top-of-the-line TM798 is structurally larger and heavier and has more features than the other models. Its unique features include a bright blue backlit LCD console, quick speed and incline keys, a wireless heart rate monitor with telemetric chest strap, remote speed and incline controls, and an anatomical figure that specifies which muscles are minimally and maximally activated. This model features a nonfolding platform base that is designed to handle rigorous, frequent running; the TM798 is therefore appealing to someone who is a power walker or a runner. The selling price is $2,500.

As a first step, the market research team at AdRight is assigned the task of identifying the profile of the typical customer for each treadmill product offered by CardioGood Fitness. The market research team decides to collect data on individuals who purchased a treadmill at a CardioGood Fitness retail store during the prior three months.

The team decides to use both business transactional data and the results of a personal profile survey that every purchaser completes as their sources of data. The team identifies the following customer variables to collect and use for this study:product purchased - TM195, TM498, or TM798; gender; age, in years; education, in years; relationship status, single or partnered; annual household income in dollars; the number of times the customer plan to use the treadmill each week, the number of miles the customer expects to walk/run each week; and self-rated fitness value on a 1 to 5 scale, where 1 is poor shape and 5 is excellent shape.

With this background information in mind, senior management at CardioGood Fitness has asked the AdRight Agency to answer the following five questions

DATA:

Product	Age	Gender	Education	Marital Status	Usage	Fitness	Income	Miles
TM195	18	Male	14	Single	3	4	29562	112
TM195	19	Male	15	Single	2	3	31836	75
TM195	19	Female	14	Partnered	4	3	30699	66
TM195	19	Male	12	Single	3	3	32973	85
TM195	20	Male	13	Partnered	4	2	35247	47
TM195	20	Female	14	Partnered	3	3	32973	66
TM195	21	Female	14	Partnered	3	3	35247	75
TM195	21	Male	13	Single	3	3	32973	85
TM195	21	Male	15	Single	5	4	35247	141
TM195	21	Female	15	Partnered	2	3	37521	85
TM195	22	Male	14	Single	3	3	36384	85
TM195	22	Female	14	Partnered	3	2	35247	66
TM195	22	Female	16	Single	4	3	36384	75
TM195	22	Female	14	Single	3	3	35247	75
TM195	23	Male	16	Partnered	3	1	38658	47
TM195	23	Male	16	Partnered	3	3	40932	75
TM195	23	Female	14	Single	2	3	34110	103
TM195	23	Male	16	Partnered	4	3	39795	94
TM195	23	Female	16	Single	4	3	38658	113
TM195	23	Female	15	Partnered	2	2	34110	38
TM195	23	Male	14	Single	4	3	38658	113
TM195	23	Male	16	Single	4	3	40932	94
TM195	24	Female	16	Single	4	3	42069	94
TM195	24	Female	16	Partnered	5	5	44343	188
TM195	24	Male	14	Single	2	3	45480	113
TM195	24	Male	13	Partnered	3	2	42069	47
TM195	24	Female	16	Single	4	3	46617	75
TM195	25	Female	14	Partnered	3	3	48891	75
TM195	25	Male	14	Partnered	2	3	45480	56
TM195	25	Female	14	Partnered	2	2	53439	47
TM195	25	Female	14	Partnered	3	3	39795	85
TM195	25	Male	16	Single	3	4	40932	113
TM195	25	Female	16	Partnered	2	2	40932	47
TM195	25	Male	16	Single	3	3	43206	85
TM195	26	Female	14	Partnered	3	4	44343	113
TM195	26	Female	16	Partnered	4	3	52302	113
TM195	26	Male	16	Partnered	2	2	53439	47
TM195	26	Male	16	Partnered	3	3	51165	85
TM195	26	Female	16	Single	3	3	36384	66
TM195	26	Male	16	Partnered	4	4	44343	132
TM195	26	Male	16	Single	3	3	50028	85
TM195	27	Female	14	Partnered	3	2	45480	66
TM195	27	Male	16	Single	4	3	54576	85
TM195	27	Female	14	Partnered	2	3	45480	56
TM195	28	Female	14	Partnered	2	3	46617	56
TM195	28	Female	16	Partnered	2	3	52302	66
TM195	28	Male	14	Single	3	3	52302	103
TM195	28	Female	14	Partnered	3	3	54576	94
TM195	28	Male	14	Single	4	3	54576	113
TM195	28	Female	16	Partnered	3	3	51165	56
TM195	29	Male	18	Partnered	3	3	68220	85
TM195	29	Female	14	Partnered	2	2	46617	38
TM195	29	Female	16	Partnered	4	3	50028	94
TM195	30	Male	14	Partnered	4	4	46617	141
TM195	30	Male	14	Single	3	3	54576	85
TM195	31	Male	14	Partnered	2	2	54576	47
TM195	31	Female	14	Single	2	2	45480	47
TM195	32	Female	14	Single	3	4	46617	113
TM195	32	Male	14	Partnered	4	3	52302	85
TM195	33	Female	16	Single	2	2	55713	38
TM195	33	Female	16	Partnered	3	3	46617	85
TM195	34	Male	16	Single	4	5	51165	169
TM195	34	Female	16	Single	2	2	52302	66
TM195	35	Male	16	Partnered	4	3	48891	85
TM195	35	Female	16	Partnered	3	3	60261	94
TM195	35	Female	18	Single	3	3	67083	85
TM195	36	Male	12	Single	4	3	44343	94
TM195	37	Female	16	Partnered	3	3	37521	85
TM195	38	Male	16	Partnered	3	3	46617	75
TM195	38	Female	14	Partnered	2	3	54576	56
TM195	38	Male	14	Single	2	3	52302	56
TM195	38	Male	16	Partnered	3	3	56850	75
TM195	39	Male	16	Partnered	4	4	59124	132
TM195	40	Male	16	Partnered	3	3	61398	66
TM195	41	Male	16	Partnered	4	3	54576	103
TM195	43	Male	16	Partnered	3	3	53439	66
TM195	44	Female	16	Single	3	4	57987	75
TM195	46	Female	16	Partnered	3	2	60261	47
TM195	47	Male	16	Partnered	4	3	56850	94
TM195	50	Female	16	Partnered	3	3	64809	66
TM498	19	Male	14	Single	3	3	31836	64
TM498	20	Male	14	Single	2	3	32973	53
TM498	20	Female	14	Partnered	3	3	34110	106
TM498	20	Male	14	Single	3	3	38658	95
TM498	21	Female	14	Partnered	5	4	34110	212
TM498	21	Male	16	Partnered	2	2	34110	42
TM498	21	Male	12	Partnered	2	2	32973	53
TM498	23	Male	14	Partnered	3	3	36384	95
TM498	23	Male	14	Partnered	3	3	38658	85
TM498	23	Female	16	Single	3	3	45480	95
TM498	23	Male	16	Partnered	4	3	45480	127
TM498	23	Female	16	Partnered	3	2	43206	74
TM498	23	Female	14	Single	3	2	40932	53
TM498	23	Male	16	Partnered	3	3	45480	64
TM498	24	Female	14	Single	3	2	40932	85
TM498	24	Male	14	Single	3	4	48891	106
TM498	24	Female	16	Single	3	3	50028	106
TM498	25	Female	14	Partnered	2	3	45480	85
TM498	25	Female	14	Single	3	4	43206	127
TM498	25	Male	16	Partnered	2	2	52302	42
TM498	25	Female	14	Partnered	5	3	47754	106
TM498	25	Male	14	Single	3	3	45480	95
TM498	25	Female	14	Single	2	3	43206	64
TM498	25	Male	14	Partnered	4	3	45480	170
TM498	25	Male	14	Partnered	3	4	43206	106
TM498	25	Male	16	Partnered	2	3	50028	53
TM498	25	Female	14	Single	2	2	45480	42
TM498	25	Male	14	Single	4	3	48891	127
TM498	26	Female	16	Partnered	4	3	45480	85
TM498	26	Female	16	Single	4	4	50028	127
TM498	26	Male	16	Single	4	3	51165	106
TM498	27	Male	14	Single	4	2	45480	53
TM498	29	Female	14	Partnered	3	3	51165	95
TM498	30	Female	14	Single	3	3	57987	74
TM498	30	Female	13	Single	4	3	46617	106
TM498	31	Male	16	Partnered	3	3	52302	95
TM498	31	Female	16	Partnered	2	3	51165	64
TM498	31	Female	18	Single	2	1	65220	21
TM498	32	Male	16	Single	4	3	60261	127
TM498	32	Male	16	Partnered	3	3	53439	95
TM498	33	Male	13	Partnered	4	4	53439	170
TM498	33	Female	16	Partnered	2	3	50028	85
TM498	33	Male	16	Partnered	3	3	51165	95
TM498	33	Female	16	Partnered	5	3	53439	95
TM498	33	Female	18	Single	3	4	47754	74
TM498	34	Female	16	Partnered	4	3	64809	95
TM498	34	Male	16	Partnered	3	4	59124	85
TM498	34	Male	15	Single	3	3	67083	85
TM498	35	Female	14	Partnered	3	2	52302	53
TM498	35	Male	16	Partnered	3	2	53439	53
TM498	35	Female	16	Single	3	2	50028	64
TM498	35	Male	16	Partnered	3	3	53439	95
TM498	37	Female	16	Partnered	2	3	48891	85
TM498	38	Female	16	Partnered	4	3	62535	85
TM498	38	Male	16	Partnered	3	3	59124	106
TM498	40	Female	16	Partnered	3	3	61398	85
TM498	40	Female	16	Single	3	3	57987	85
TM498	40	Male	16	Partnered	3	3	64809	95
TM498	45	Male	16	Partnered	2	2	54576	42
TM498	48	Male	16	Partnered	2	3	57987	64
TM798	22	Male	14	Single	4	3	48658	106
TM798	22	Male	16	Single	3	5	54781	120
TM798	22	Male	18	Single	4	5	48556	200
TM798	23	Male	16	Single	4	5	58516	140
TM798	23	Female	18	Single	5	4	53536	100
TM798	23	Male	16	Single	4	5	48556	100
TM798	24	Male	16	Single	4	5	61006	100
TM798	24	Male	18	Partnered	4	5	57271	80
TM798	24	Female	16	Single	5	5	52291	200
TM798	24	Male	16	Single	5	5	49801	160
TM798	25	Male	16	Partnered	4	5	49801	120
TM798	25	Male	16	Partnered	4	4	62251	160
TM798	25	Female	18	Partnered	5	5	61006	200
TM798	25	Male	18	Partnered	4	3	64741	100
TM798	25	Male	18	Partnered	6	4	70966	180
TM798	25	Male	18	Partnered	6	5	75946	240
TM798	25	Male	20	Partnered	4	5	74701	170
TM798	26	Female	21	Single	4	3	69721	100
TM798	26	Male	16	Partnered	5	4	64741	180
TM798	27	Male	16	Partnered	4	5	83416	160
TM798	27	Male	18	Single	4	3	88396	100
TM798	27	Male	21	Partnered	4	4	90886	100
TM798	28	Female	18	Partnered	6	5	92131	180
TM798	28	Male	18	Partnered	7	5	77191	180
TM798	28	Male	18	Single	6	5	88396	150
TM798	29	Male	18	Single	5	5	52290	180
TM798	29	Male	14	Partnered	7	5	85906	300
TM798	30	Female	16	Partnered	6	5	90886	280
TM798	30	Male	18	Partnered	5	4	103336	160
TM798	30	Male	18	Partnered	5	5	99601	150
TM798	31	Male	16	Partnered	6	5	89641	260
TM798	33	Female	18	Partnered	4	5	95866	200
TM798	34	Male	16	Single	5	5	92131	150
TM798	35	Male	16	Partnered	4	5	92131	360
TM798	38	Male	18	Partnered	5	5	104581	150
TM798	40	Male	21	Single	6	5	83416	200
TM798	42	Male	18	Single	5	4	89641	200
TM798	45	Male	16	Single	5	5	90886	160
TM798	47	Male	18	Partnered	4	5	104581	120
TM798	48	Male	18	Partnered	4	5	95508	180