Question

Health insurers are beginning to offer telemedicine services online that replace the common office visit. A company provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. The company claims that users of its online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by the company.

87	29	35	100
78	50	51	44
35	71	43	91
88	69	68	73
88	95	48	77

Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings in dollars for a televisit to the doctor as opposed to an office visit. (Round your answers to the nearest cent.)

$  to $

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2
	87	441
	78	144
	35	961
	88	484
	88	484
	29	1369
	50	256
	71	25
	69	9
	95	841
	35	961
	51	225
	43.0	529
	68	4
	48	324
	100	1156
	44	484
	91	625
	73	49
	77	121
Total	1320	9492

Mean X̅ = Σ Xi / n
X̅ = 1320 / 20 = 66
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 9492 / 20 -1 ) = 22.3513

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
Critical value t(α/2, n-1) = t(0.05 /2, 20- 1 ) = 2.093 ( From t table )
66 ± t(0.05/2, 20 -1) * 22.3513/√(20)
Lower Limit = 66 - t(0.05/2, 20 -1) 22.3513/√(20)
Lower Limit = 55.54
Upper Limit = 66 + t(0.05/2, 20 -1) 22.3513/√(20)
Upper Limit = 76.46
95% Confidence interval is ( $55.54 , $76.46 )