Question

Congo Incorporated claimed in its annual report that "the typical customer spends $65 per month on streaming apps." A sample of 12 subscribers revealed the following amounts spent last month.

$57

$69

$60

$68

$66

$65

$63

$64

$67

$59

$58

$58

(a)	What is the point estimate of the population mean? (Round your answer to 3 decimal places.)

Population mean

$

(b)	Determine the 90% confidence interval for the population mean. (Round your answers to 2 decimal places.)

Confidence interval

$  and $

(c)	Is the company's claim that the "typical customer" spends $65 per month reasonable?
	Yes No

Answer 1

Sample size : Number of subscribers in the sample : n= 12

Sample data : x_i : Amount spent by the i^th subscriber

(a) point estimate of the population mean is the sample mean :

Sample mean :

point estimate of the population mean = 62.833

(b)

Formula for Confidence Interval for Population mean when population Standard deviation is not known

s: Sample standard deviation

xi
57	-5.8333	34.0278
69	6.1667	38.0278
60	-2.8333	8.0278
68	5.1667	26.6944
66	3.1667	10.0278
65	2.1667	4.6944
63	0.1667	0.0278
64	1.1667	1.3611
67	4.1667	17.3611
59	-3.8333	14.6944
58	-4.8333	23.3611
58	-4.8333	23.3611
		201.6667

for 90% confidence level = (100-90)/100 =0.1

/2 = 0.05

Degrees of freedom = n-1 =12-1 =11

t_/2,n-1 = t_0.05,11 = 1.7959

90% confidence interval for the population mean :

90% confidence interval for the population mean = (60.6132 , 65.0528)

(c) Is the company's claim that the "typical customer" spends $65 per month reasonable?

As 65 is within (60.6132 < 65 < 65.0528) the confidence interval ; Yes, the company's claim that the "typical customer" spends $65 per month reasonable

Answer : Yes