Question

Count	iPhone User Id	Price Willing to Pay
1	101	1150
2	204	800
3	205	1050
4	405	1400
5	701	1050
6	105	1350
7	98	700
8	12	1450
9	37	800
10	55	650
11	68	750
12	31	1200
13	90	500
14	92	950
15	447	1050
16	778	1150

You are hired by Google to research how much people are willing to pay for a new cell phone in US. They are especially interested to know if their new phone, Pixel 3, should be priced similarly to Apple’s iPhone Xs. Google believes that there is a difference between what Android and iPhone users are willing to pay for high-end phones. You are hired to answer this question. Part I: To analyze iPhone users your team randomly selects 16 individuals. See attached data file.

a) Compute sample mean and sample standard deviation for iPhone users

b) Compute 5-number summary for iPhone users

c) Find the 90% confidence interval for the average phone price iPhone users are willing to pay. How do you interpret it?

Answer 1

sample mean=sum/n==3429/16=214.3125

sample standard deviation=sqrt(sum((x-)²)/(n-1))=sqrt(866799.4375/(16-1))=240.39

Count	iPhone User Id(x)	(x-214.3125)2	x-214.3125
1	101	-113.31	12839.72
2	204	-10.31	106.35
3	205	-9.31	86.72
4	405	190.69	36361.72
5	701	486.69	236864.72
6	105	-109.31	11949.22
7	98	-116.31	13528.60
8	12	-202.31	40930.35
9	37	-177.31	31439.72
10	55	-159.31	25380.47
11	68	-146.31	21407.35
12	31	-183.31	33603.47
13	90	-124.31	15453.60
14	92	-122.31	14960.35
15	447	232.69	54143.47
16	778	563.69	317743.60
sum=	3429	0	866799.4375
n=	16
sample mean=sum/n=	214.3125
sample sd=	240.3884963

(b) five number summery using R is given as

x=c(101,204,205,405,701,105,98,12,37,55,68,31,90,92,447,778)
> summary(x)
Min. 1st Qu. Median 3rd Qu. Max.
12.00 64.75 99.50 255.00 778.00

(c) (1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*s/sqrt(n)

90% confidence interval =214.3125±t(0.1/2, n-1)*240.39/sqrt(16)=214.3125±1.75*240.39/sqrt(16)=

214.3125±105.35=(108.96,319.67)

n=	16
sample mean=	214.3125
s=	240.39

	t-value	margin of error	lower limit	upper limit
95% confidence interval	2.13	128.09	86.22	342.41
99% confidence interval	2.95	177.09	37.22	391.40
90% confidence interval	1.75	105.35	108.96	319.67