Question

A sample of 20 cars, including measurements of fuel consumption (city mi/gal and highway mi/gal), weight (pounds), number of cylinders, engine displacement (in liters), amount of greenhouse gases emitted (in tons/year), and amount of tailpipe emissions of NO_x (in lb/yr).

CAR	CITY	HWY	WEIGHT	CYLINDERS	DISPLACEMENT	MAN/AUTO	GHG	NOX
Chev. Camaro	19	30	3545	6	3.8	M	12	34.4
Chev. Cavalier	23	31	2795	4	2.2	A	10	25.1
Dodge Neon	23	32	2600	4	2	A	10	25.1
Ford Taurus	19	27	3515	6	3	A	12	25.1
Honda Accord	23	30	3245	4	2.3	A	11	25.1
Lincoln Cont.	17	24	3930	8	4.6	A	14	25.1
Mercury Mystique	20	29	3115	6	2.5	A	12	34.4
Mitsubishi Eclipse	22	33	3235	4	2	M	10	25.1
Olds. Aurora	17	26	3995	8	4	A	13	34.4
Pontiac Grand Am	22	30	3115	4	2.4	A	11	25.1
Toyota Camry	23	32	3240	4	2.2	M	10	25.1
Cadillac DeVille	17	26	4020	8	4.6	A	13	34.4
Chev. Corvette	18	28	3220	8	5.7	M	12	34.4
Chrysler Sebring	19	27	3175	6	2.5	A	12	25.1
Ford Mustang	20	29	3450	6	3.8	M	12	34.4
BMW 3-Series	19	27	3225	6	2.8	A	12	34.4
Ford Crown Victoria	17	24	3985	8	4.6	A	14	25.1
Honda Civic	32	37	2440	4	1.6	M	8	25.1
Mazda Protege	29	34	2500	4	1.6	A	9	25.1
Hyundai Accent	28	37	2290	4	1.5	A	9	34.4

Part IV

The ultimate goal in any statistical study is to make inferences about the population using the sample information. This is called inferential statistics.

3. Suppose we are also interested in the proportion of car models that have 4 cylinders in a sample. Suppose it is known than about 50% of all car models have 4 cylinders. Use the dataset CYLINDERS as a sample, and find the probability of randomly selecting a sample of 20 car models that contains more 4 cylinder cars than the number of 4 cylinder cars in dataset CYLINDERS. Find the sample proportion, determine the sampling distribution (normal), and find the probability

Answer 1

Result:

Part IV

The ultimate goal in any statistical study is to make inferences about the population using the sample information. This is called inferential statistics.

3. Suppose we are also interested in the proportion of car models that have 4 cylinders in a sample. Suppose it is known than about 50% of all car models have 4 cylinders. Use the dataset CYLINDERS as a sample, and find the probability of randomly selecting a sample of 20 car models that contains more 4 cylinder cars than the number of 4 cylinder cars in dataset CYLINDERS. Find the sample proportion, determine the sampling distribution (normal), and find the probability

One-Way Summary Table
Count of CYLINDERS
CYLINDERS	Total
4	9
6	6
8	5
Grand Total	20

Proportion of models that contains more 4 cylinder = 9/20 = 0.45

n=20

Binomial Probabilities
Data
Sample size	20
Probability of an event of interest	0.45
Statistics
Mean	9
Variance	4.9500
Standard deviation	2.2249
Binomial Probabilities Table
	X	P(X)	P(<=X)	P(<X)	P(>X)	P(>=X)
	0	0.0000	0.0000	0.0000	1.0000	1.0000
	1	0.0001	0.0001	0.0000	0.9999	1.0000
	2	0.0008	0.0009	0.0001	0.9991	0.9999
	3	0.0040	0.0049	0.0009	0.9951	0.9991
	4	0.0139	0.0189	0.0049	0.9811	0.9951
	5	0.0365	0.0553	0.0189	0.9447	0.9811
	6	0.0746	0.1299	0.0553	0.8701	0.9447
	7	0.1221	0.2520	0.1299	0.7480	0.8701
	8	0.1623	0.4143	0.2520	0.5857	0.7480
	9	0.1771	0.5914	0.4143	0.4086	0.5857
	10	0.1593	0.7507	0.5914	0.2493	0.4086
	11	0.1185	0.8692	0.7507	0.1308	0.2493
	12	0.0727	0.9420	0.8692	0.0580	0.1308
	13	0.0366	0.9786	0.9420	0.0214	0.0580
	14	0.0150	0.9936	0.9786	0.0064	0.0214
	15	0.0049	0.9985	0.9936	0.0015	0.0064
	16	0.0013	0.9997	0.9985	0.0003	0.0015
	17	0.0002	1.0000	0.9997	0.0000	0.0003
	18	0.0000	1.0000	1.0000	0.0000	0.0000
	19	0.0000	1.0000	1.0000	0.0000	0.0000
	20	0.0000	1.0000	1.0000	0.0000	0.0000