Date Day Time Region Card Type Gender Buy Category Items Ordered Total Cost High Item 6-Mar Sun Morning West AJ Female High 4 $136.97 $79.97 6-Mar Sun Morning West Other Female Medium 1 $25.55 $25.55 6-Mar Sun Afternoon West AJ Female Medium 5 $113.95 $90.47 6-Mar Sun Afternoon NorthEast Other Female Low 1 $6.82 $6.82 6-Mar Sun Afternoon West AJ Male Medium 4 $147.32 $83.21 6-Mar Sun Afternoon NorthEast Other Female Medium 5 $142.15 $50.90 7-Mar Mon Evening West Other Male Low 1 $18.65 $18.65 7-Mar Mon Evening South Other Male High 4 $178.34 $161.93 7-Mar Mon Evening West Other Male Low 2 $25.83 $15.91 8-Mar Tue Morning MidWest Other Female Low 1 $18.13 $18.13 8-Mar Tue Morning NorthEast AJ Female Medium 2 $54.52 $54.38 8-Mar Tue Afternoon South Other Male Medium 2 $61.93 $56.32 9-Mar Wed Morning NorthEast AJ Male High 3 $147.68 $96.64 9-Mar Wed Afternoon NorthEast Other Male Low 1 $27.24 $27.24 10-Mar Thu Morning West Other Female Low 3 $46.18 $44.27 10-Mar Thu Afternoon West Other Male Low 5 $107.44 $91.64 10-Mar Thu Afternoon South AJ Female Medium 6 $96.53 $93.68 10-Mar Thu Afternoon West AJ Female Medium 4 $77.44 $77.28 11-Mar Fri Morning South Other Male Low 1 $15.19 $15.19 11-Mar Fri Afternoon South Other Male Medium 1 $45.52 $45.52 12-Mar Sat Morning West Other Male High 4 $157.05 $146.28 12-Mar Sat Afternoon West Other Male Medium 2 $51.95 $30.40 12-Mar Sat Evening West AJ Female High 9 $429.98 $381.33 13-Mar Sun Afternoon South Other Female Low 1 $33.37 $33.37 13-Mar Sun Evening West Other Male Medium 3 $71.84 $34.13 14-Mar Mon Morning NorthEast AJ Female Medium 5 $139.51 $133.11 14-Mar Mon Afternoon South Other Male Medium 3 $78.46 $58.53 14-Mar Mon Evening MidWest Other Male High 3 $125.13 $103.31 15-Mar Tue Afternoon MidWest Other Male Medium 1 $14.76 $14.76 15-Mar Tue Afternoon South AJ Female High 2 $83.38 $71.02 16-Mar Wed Morning West Other Female High 3 $104.91 $47.79 This dataset shows a sample of customers’ orders from AJ Madison, an online retailer of electronic appliances. a)Calculate a 95% confidence interval for the proportion of all customers whose total cost is more than $100. b)Calculate a 99% confidence interval for the mean total cost for NorthEast Transactions. c)Calculate a 95% confidence interval for the standard deviation of total cost for all customers (assuming that total cost follows normal distribution).

Date Day Time Region Card Type Gender Buy Category Items Ordered Total Cost High Item 6-Mar Sun Morning West AJ Female High 4 $136.97 $79.97 6-Mar Sun Morning West Other Female Medium 1 $25.55 $25.55 6-Mar Sun Afternoon West AJ Female Medium 5 $113.95 $90.47 6-Mar Sun Afternoon NorthEast Other Female Low 1 $6.82 $6.82 6-Mar Sun Afternoon West AJ Male Medium 4 $147.32 $83.21 6-Mar Sun Afternoon NorthEast Other Female Medium 5 $142.15 $50.90 7-Mar Mon Evening West Other Male Low 1 $18.65 $18.65 7-Mar Mon Evening South Other Male High 4 $178.34 $161.93 7-Mar Mon Evening West Other Male Low 2 $25.83 $15.91 8-Mar Tue Morning MidWest Other Female Low 1 $18.13 $18.13 8-Mar Tue Morning NorthEast AJ Female Medium 2 $54.52 $54.38 8-Mar Tue Afternoon South Other Male Medium 2 $61.93 $56.32 9-Mar Wed Morning NorthEast AJ Male High 3 $147.68 $96.64 9-Mar Wed Afternoon NorthEast Other Male Low 1 $27.24 $27.24 10-Mar Thu Morning West Other Female Low 3 $46.18 $44.27 10-Mar Thu Afternoon West Other Male Low 5 $107.44 $91.64 10-Mar Thu Afternoon South AJ Female Medium 6 $96.53 $93.68 10-Mar Thu Afternoon West AJ Female Medium 4 $77.44 $77.28 11-Mar Fri Morning South Other Male Low 1 $15.19 $15.19 11-Mar Fri Afternoon South Other Male Medium 1 $45.52 $45.52 12-Mar Sat Morning West Other Male High 4 $157.05 $146.28 12-Mar Sat Afternoon West Other Male Medium 2 $51.95 $30.40 12-Mar Sat Evening West AJ Female High 9 $429.98 $381.33 13-Mar Sun Afternoon South Other Female Low 1 $33.37 $33.37 13-Mar Sun Evening West Other Male Medium 3 $71.84 $34.13 14-Mar Mon Morning NorthEast AJ Female Medium 5 $139.51 $133.11 14-Mar Mon Afternoon South Other Male Medium 3 $78.46 $58.53 14-Mar Mon Evening MidWest Other Male High 3 $125.13 $103.31 15-Mar Tue Afternoon MidWest Other Male Medium 1 $14.76 $14.76 15-Mar Tue Afternoon South AJ Female High 2 $83.38 $71.02 16-Mar Wed Morning West Other Female High 3 $104.91 $47.79 This dataset shows a sample of customers’ orders from AJ Madison, an online retailer of electronic appliances. a)Calculate a 95% confidence interval for the proportion of all customers whose total cost is more than $100. b)Calculate a 99% confidence interval for the mean total cost for NorthEast Transactions. c)Calculate a 95% confidence interval for the standard deviation of total cost for all customers (assuming that total cost follows normal distribution).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Date	Day	Time	Region	Card Type	Gender	Buy Category	Items Ordered	Total Cost	High Item
6-Mar	Sun	Morning	West	AJ	Female	High	4	$136.97	$79.97
6-Mar	Sun	Morning	West	Other	Female	Medium	1	$25.55	$25.55
6-Mar	Sun	Afternoon	West	AJ	Female	Medium	5	$113.95	$90.47
6-Mar	Sun	Afternoon	NorthEast	Other	Female	Low	1	$6.82	$6.82
6-Mar	Sun	Afternoon	West	AJ	Male	Medium	4	$147.32	$83.21
6-Mar	Sun	Afternoon	NorthEast	Other	Female	Medium	5	$142.15	$50.90
7-Mar	Mon	Evening	West	Other	Male	Low	1	$18.65	$18.65
7-Mar	Mon	Evening	South	Other	Male	High	4	$178.34	$161.93
7-Mar	Mon	Evening	West	Other	Male	Low	2	$25.83	$15.91
8-Mar	Tue	Morning	MidWest	Other	Female	Low	1	$18.13	$18.13
8-Mar	Tue	Morning	NorthEast	AJ	Female	Medium	2	$54.52	$54.38
8-Mar	Tue	Afternoon	South	Other	Male	Medium	2	$61.93	$56.32
9-Mar	Wed	Morning	NorthEast	AJ	Male	High	3	$147.68	$96.64
9-Mar	Wed	Afternoon	NorthEast	Other	Male	Low	1	$27.24	$27.24
10-Mar	Thu	Morning	West	Other	Female	Low	3	$46.18	$44.27
10-Mar	Thu	Afternoon	West	Other	Male	Low	5	$107.44	$91.64
10-Mar	Thu	Afternoon	South	AJ	Female	Medium	6	$96.53	$93.68
10-Mar	Thu	Afternoon	West	AJ	Female	Medium	4	$77.44	$77.28
11-Mar	Fri	Morning	South	Other	Male	Low	1	$15.19	$15.19
11-Mar	Fri	Afternoon	South	Other	Male	Medium	1	$45.52	$45.52
12-Mar	Sat	Morning	West	Other	Male	High	4	$157.05	$146.28
12-Mar	Sat	Afternoon	West	Other	Male	Medium	2	$51.95	$30.40
12-Mar	Sat	Evening	West	AJ	Female	High	9	$429.98	$381.33
13-Mar	Sun	Afternoon	South	Other	Female	Low	1	$33.37	$33.37
13-Mar	Sun	Evening	West	Other	Male	Medium	3	$71.84	$34.13
14-Mar	Mon	Morning	NorthEast	AJ	Female	Medium	5	$139.51	$133.11
14-Mar	Mon	Afternoon	South	Other	Male	Medium	3	$78.46	$58.53
14-Mar	Mon	Evening	MidWest	Other	Male	High	3	$125.13	$103.31
15-Mar	Tue	Afternoon	MidWest	Other	Male	Medium	1	$14.76	$14.76
15-Mar	Tue	Afternoon	South	AJ	Female	High	2	$83.38	$71.02
16-Mar	Wed	Morning	West	Other	Female	High	3	$104.91	$47.79

This dataset shows a sample of customers’ orders from AJ Madison, an online retailer of electronic appliances.

a)Calculate a 95% confidence interval for the proportion of all customers whose total cost is more than $100.

b)Calculate a 99% confidence interval for the mean total cost for NorthEast Transactions.

c)Calculate a 95% confidence interval for the standard deviation of total cost for all customers (assuming that total cost follows normal distribution).

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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