Question

The data shown below ($), for a sample of 20 guest bills for Danvers-Hilton resort hotel for a weekend. Assume the population is approximately normal. Develop a 95% confidence interval for the mean guest bills of Danvers-Hilton resort hotel. 1905 2962 2545 2529 2627 2725 2184 2525 2442 2857 2677 2332 2370 2312 2675 2600 3112 2545 2981 2115

: Upper Bound: 2478.35, Lower Bound: 2147.25

Upper Bound: 2758.95, Lower Bound: 2409.98

Upper Bound: 2714.95, Lower Bound: 2387.05

Upper Bound: 2692.02, Lower Bound: 2258.25

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2
	1905	417316
	2962	168921
	2545	36
	2529	484
	2627	5776
	2725	30276
	2184	134689
	2525	676
	2442	11881
	2857	93636
	2677	15876
	2332	47961
	2370	32761
	2312	57121
	2675	15376
	2600	2401
	3112	314721
	2545	36
	2981	184900
	2115	190096
Total	51020	1724940

Mean X̅ = Σ Xi / n
X̅ = 51020 / 20 = 2551
Sample Standard deviation S_X = √ ( (Xi - X̅ )2 / n - 1 )
S_X = √ ( 1724940 / 20 -1 ) = 301.3077

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 20- 1 ) = 2.093
2551 ± t(0.05/2, 20 -1) * 301.3077/√(20)
Lower Limit = 2551 - t(0.05/2, 20 -1) 301.3077/√(20)
Lower Limit = 2409.9837
Upper Limit = 2551 + t(0.05/2, 20 -1) 301.3077/√(20)
Upper Limit = 2692.0163
95% Confidence interval is ( 2409.98 , 2692.02 )